Если у вас возникли сложности с курсовой, контрольной, дипломной, рефератом, отчетом по практике, научно-исследовательской и любой другой работой - мы готовы помочь.
Предоплата всего
Подписываем
|
ВМ 3 ИДЗ 1 2012 Неопределенный интеграл. Для выработки навыков интегрирования решить примеры из сб Г.Н.Берман Гл V1 &1 - 3 по силе, но не менее 50% (без сдачи). Для контроля: |
||||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
Задача 5 |
Задача 6 |
Задача 7 |
Задача 8 |
|
1 |
∫ e3x+2 cos(x-1) dx |
∫ tg4x dx |
∫ {B/(1-3sinx+cosx)} dx |
∫{1/(x3+x2-4x-4)} dx |
∫ {(x+3)/(9x2-3)} dx |
∫{[(3√x2 )+2x+1]/√(2x)} dx |
∫ {x/√(x2 +2x+10)} dx |
∫{(ex +1)/(9+e2x)} dx |
|
2 |
∫ e2x-1 sin(x+2) dx |
∫ сtg4x dx |
∫ {2/(2-3sinx-cosx)} dx |
∫{2/(x3+2x2-x-2)} dx |
∫ {(x-2)/(4x2+1)} dx |
∫{[(3√x2 )+3x-2]/√(3x)} dx |
∫ {1/(х+1)√(x2 +2x+2)} dx |
∫{( ex -2)/√(4+e2x )} dx |
|
3 |
∫ ex-4 cos(2x) dx |
∫ tg5x dx |
∫ {3/(3+3sinx+cosx)} dx |
∫{3/(x3+3x2-x-3)} dx |
∫ {(2x+5)/(x2-5)} dx |
∫{[(3√x2 )-4x+3]/√(5x)} dx |
∫ {2x/√(x2 -2x+10)} dx |
∫{( ex +3)/(3+e2x )} dx |
|
4 |
∫ ex+5 sin(3x) dx |
∫ сtg5x dx |
∫ {4/(4+3sinx-cosx)} dx |
∫{4/(x3+4x2+x-6)} dx |
∫ {(4x-7)/(x2+4)} dx |
∫{[(3√x2 )-5x-4]/√(7x)} dx |
∫ {2/(х+1)√(x2 +2x)} dx |
∫{( ex -4)/√( 2+e2x )} dx |
|
5 |
∫ ex+1 cos(x-3) dx |
∫ tg6x dx |
∫ {5/(5-sinx+3cosx)} dx |
∫{5/(x3+5x2-4x-20)} dx |
∫ {(6x+7)/(x2-3)} dx |
∫{[(3√x2 )+6x+5]/√x} dx |
∫ {4/3(х+1)√(3-x2 -2x)} dx |
∫{( ex +5)/( 1+e2x)} dx |
|
6 |
∫ ex-2 sin(x+1) dx |
∫ сtg6x dx |
∫ {6/(5-sinx-3cosx)} dx |
∫{6/(x3+6x2+3x-10)} dx |
∫ {(4x+3)/(x2-4)} dx |
∫{[(3√x2 )+7x-6]/√(2x)} dx |
∫ {x/√(x2 +4x+13)} dx |
∫{( ex -6)/√( 1+e2x )} dx |
|
7 |
∫ e3+x cos(x-4) dx |
∫ 7tg3x dx |
∫ {7/(4+sinx+3cosx)} dx |
∫{7/(x3+7x2+7x-15)} dx |
∫ {(8x+7)/(4x2+3)} dx |
∫{[(3√x2 )-8x+7]/√(3x)} dx |
∫ {1/(х-1)√(x2 -2x+2)} dx |
∫{( ex +7)/√( 2+e2x )} dx |
|
8 |
∫ e2-x sin(x+5) dx |
∫ 8сtg2x dx |
∫ {8/(3+sinx-3cosx)} dx |
∫{8/(x3+8x2+11x-20)} dx |
∫ {(2x+13)/(4x2-3)} dx |
∫{[(3√x2 )-9x-8]/√(5x)} dx |
∫ {2x/√(x2 -4x+13)} dx |
∫{( ex -8)/√( 3+e2x )} dx |
|
9 |
∫ ex-2 cos(x-1) dx |
∫ 9tg4x dx |
∫ {9/(2-2sinx+cosx)} dx |
∫{9/(x3+9x2+8x-60)} dx |
∫ {(2x-9)/(x2+4)} dx |
∫{[(3√x2 )+ x+9]/√(7x)} dx |
∫ {2/(х-1)√(x2 -2x)} dx |
∫{( ex +9)/√( 4+e2x )} dx |
|
10 |
∫ ex-3 sin(x-2) dx |
∫ 10сtg2x dx |
∫ {10/(1-2sinx-cosx)} dx |
∫{10/(x3+10x2+19x-30)} dx |
∫ {(10x+23)/(4x2+9)} dx |
∫{[(3√x2 )+9x-10]/√x } dx |
∫ {4/3(х-1)√(2х -x2 )} dx |
∫{( ex -10)/( 9+e2x) } dx |
|
11 |
∫ ex+2 cos(x+2) dx |
∫ 11tg4x dx |
∫ {11/(1+2sinx+cosx)} dx |
∫{11/(x3+11x2+38x+40)} dx |
∫ {(x+3)/(x2-16)} dx |
∫{[(3√x2 )-8x+11]/√(2x)} dx |
∫ {x/√(x2 +2x-8)} dx |
∫{( ex +11)/√( 9+e2x )} dx |
|
12 |
∫ e2+x sin(x-3) dx |
∫ 12сtg4x dx |
∫ {12/(2+2sinx-cosx)} dx |
∫{12/(x3+12x2+47x+60)} dx |
∫ {(x+3)/(x2+25)} dx |
∫{[(3√x2 )-7x-12]/√(3x)} dx |
∫ {1/(х+2)√(x2 +4x+5)} dx |
∫{( ex -12)/√( 4+e2x )} dx |
|
13 |
∫ ex-3 cos(x+1) dx |
∫ tg5x dx |
∫ {13/(3-sinx+2cosx)} dx |
∫{13/(x3+13x2+52x+60)} dx |
∫ {(x+3)/(4x2-9)} dx |
∫{[(3√x2 )+6x+13]/√(5x)} dx |
∫ {2x/√(x2 -2x-8)} dx |
∫{( ex +13)/√( 3+e2x )} dx |
|
14 |
∫ ex-4 sin(x-4) dx |
∫ сtg5x dx |
∫ {14/(4-sinx-2cosx)} dx |
∫{14/(x3+14x2+63x+90)} dx |
∫ {(x+3)/(9x2+16)} dx |
∫{[(3√x2 )+5x-14]/√(7x)} dx |
∫ {2/(х+2)√(x2 +4x+3)} dx |
∫{( ex -14)/√( 2+e2x )} dx |
|
15 |
∫ ex+7 cos(x+5) dx |
∫ tg6x dx |
∫ {15/(5+sinx+2cosx)} dx |
∫{15/(x3+15x2+74x+120)} dx |
∫ {(x+3)/(x2-36)} dx |
∫{[(3√x2 )-4x+15]/√x } dx |
∫ {4/3(х+2)√(5-x2 -4x)} dx |
∫{( ex +15)/( 1+e2x) } dx |
|
16 |
∫ e2x+1 sin(x-1) dx |
∫ сtg6x dx |
∫ {16/(5+sinx-2cosx)} dx |
∫{16/(x3+16x2+79x+120)} dx |
∫ {(x+3)/(x2+4)} dx |
∫{[(3√x2 )-3x-15]/√(2x)} dx |
∫ {x/√(8-x2 -2x)} dx |
∫{( ex -15)/√( 1+e2x )} dx |
|
17 |
∫ ex+2 cos(x-4) dx |
∫ 17tg3x dx |
∫ {17/(4-sinx+cosx)} dx |
∫{17/(x3+17x2+92x+160)} dx |
∫ {(x+3)/(x2-25)} dx |
∫{[(3√x2 )+2x+14]/√(3x)} dx |
∫ {1/(х-2)√(x2 -4x+5)} dx |
∫{( ex +14)/√( 2+e2x )} dx |
|
18 |
∫ e2-x sin(x+7) dx |
∫ 18сtg3x dx |
∫ {18/(3-sinx-cosx)} dx |
∫{18/(x3+18x2+105x+200)} dx |
∫ {(8x+23)/(16x2+9)} dx |
∫{[(3√x2 )+ x-13]/√(5x)} dx |
∫ {2x/√(8-x2 +2x)} dx |
∫{( ex -13)/√( 3+e2x )} dx |
|
19 |
∫ ex-6 cos(x-2) dx |
∫ 19tg2x dx |
∫ {19/(2+2sinx+2cosx)} dx |
∫{19/(x3+19x2+118x+240)} dx |
∫ {(2x+13)/(x2-49)} dx |
∫{[(3√x2 )- x+12]/√(7x)} dx |
∫ {2/(х-2)√(x2 -4x+3)} dx |
∫{( ex +12)/√(4+e2x )} dx |
|
20 |
∫ e5-x sin(x+3) dx |
∫ 20сtg2x dx |
∫ {20/(1+2sinx-2cosx)} dx |
∫{20/(x3+20x2+131x+280)} dx |
∫ {(2x+8)/(x2+1)} dx |
∫{[(3√x2 )- 2x-11]/√x } dx |
∫ {4/3(х-2)√(5-x2 +4x)} dx |
∫{( ex -11)/( 9+e2x) } dx |
|
21 |
∫ ex cos(2x-3) dx |
∫ 21tg4x dx |
∫ {21/(1-4sinx+cosx)} dx |
∫{21/(x3+21x2+146x+336)} dx |
∫ {(2x+6)/(x2-2)} dx |
∫{[(3√x2 )+3x+10]/√(2x)} dx |
∫ {x/√(x2 +4x-5)} dx |
∫{( ex +10)/√(9+e2x )} dx |
|
22 |
∫ ex sin(3x+1) dx |
∫ 22сtg4x dx |
∫ {22/(2-4sinx-cosx)} dx |
∫{22/(x3+22x2+161x+392)} dx |
∫ {(6x-4)/(x2+9)} dx |
∫{[(3√x2 )+4x-9]/√(3x)} dx |
∫ {1/(х+1)√(x2 +2x+5)} dx |
∫{( ex -9)/√(3+e2x )} dx |
|
23 |
∫ e3x cos(x-4) dx |
∫ 23tg5x dx |
∫ {23/(3+4sinx+cosx)} dx |
∫{23/(x3+23x2+176x+448)} dx |
∫ {(4x-2)/(x2-7)} dx |
∫{[(3√x2 )-5x+8]/√(5x)} dx |
∫ {2x/√(x2 -4x-5)} dx |
∫{( ex +8)/√(4+e2x )} dx |
|
24 |
∫ e2x sin(x+5) dx |
∫ 24сtg5x dx |
∫ {24/(4+4sinx-cosx)} dx |
∫{24/(x3+24x2+191x+504)} dx |
∫ {(2x-10)/(x2+16)} dx |
∫{[(3√x2 )-6x-7]/√(7x)} dx |
∫ {2/(х+1)√(x2 +2x+3)} dx |
∫{( ex -7)/√(2+e2x )} dx |
|
25 |
∫ e3x+1 cosx dx |
∫ 25tg6x dx |
∫ {25/(5-sinx+4cosx)} dx |
∫{25/(x3+25x2+208x+576)} dx |
∫ {(8x+16)/(4x2+25)} dx |
∫{[(3√x2 )+7x+6]/√x } dx |
∫ {4/3(х+1)√(3-x2 -2x)} dx |
∫{( ex +6)/ 1+e2x )} dx |
|
26 |
∫ e2x sin2x dx |
∫ 26сtg6x dx |
∫ {26/(5-sinx-4cosx)} dx |
∫{26/(x3+26x2+225x+648)} dx |
∫ {(4x-6)/(4x2+5)} dx |
∫{[(3√x2 )+8x-5]/√(2x)} dx |
∫ {x/√(5-x2 -4x)} dx |
∫{( ex -5)/√(1+e2x )} dx |
|
27 |
∫ e3x cos2x dx |
∫ 27tg3x dx |
∫ {27/(4+sinx+4cosx)} dx |
∫{27/(x3+27x2+242x+720)} dx |
∫ {(2x-12)/(9x2+4)} dx |
∫{[(3√x2 )-9x+4]/√(3x)} dx |
∫ {1/(х-1)√(x2 -2x+5)} dx |
∫{( ex +4)/√(2+e2x )} dx |
|
28 |
∫ e2x sin3x dx |
∫ 28сtg3x dx |
∫ {28/(3+sinx-4cosx)} dx |
∫{28/(x3+28x2+261x+810)} dx |
∫ {(4x+10)/(9x2+16)} dx |
∫{[(3√x2 )- x-3]/√(5x)} dx |
∫ {4x/√(5-x2 +4x)} dx |
∫{( ex -3)/√(3+e2x )} dx |
|
29 |
∫ e3x cos5x dx |
∫ 29tg2x dx |
∫ {29/(2-3sinx+4cosx)} dx |
∫{29/(x3+18x2+105x+200)} dx |
∫ {(x+3)/(x2+25)} dx |
∫{[(3√x2 )+6x+5]/√x} dx |
∫ {2x/√(x2 -2x+10)} dx |
∫{( ex -2)/√(4+e2x )} dx |
|
30 |
∫ e2x sin2x dx |
∫ 30сtg2x dx |
∫ {30/(1-3sinx-4cosx)} dx |
∫{30/(x3+19x2+118x+240)} dx |
∫ {(x+3)/(4x2-9)} dx |
∫{[(3√x2 )+7x-6]/√(2x)} dx |
∫ {2/(х+1)√(x2 +2x)} dx |
∫{( ex +3)/(3+e2x )} dx |
|
ВМ 3 ИДЗ 2 -2012 Определенный Интеграл. |
||||||||||||||||||||||||
|
Вычисление ОИ и нахождение площадей x2 1. В задачах 1 – 4 вычислить определенный интеграл ∫ f(x) dx x1 2. В задачах 5 и 6 вычислить площадь плоской фигуры, ограниченной линиями а) Х2 / А2 + У2 / В2 = 1 ; б) У = А – В Х3, Х=0 и У=0 |
Вычисление объема тела вращения, площади поверхности и длины дуги плоской кривой 1. В задаче 1 вычислить объем тела вращения Х2 / А2 + У2 / В2 = 1 вокруг оси Ох 2. В задаче 2 вычислить площадь поверхности тела вращения У= Х3 / С вокруг оси Ох при Х1 <X < X2 3. В задаче 3 вычислить длину дуги плоской кривой { X = t6 / A; Y = B – t4 / C } между точками пересечения ее с осями координат. |
|||||||||||||||||||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
З 5, 6 |
Задача 1 |
Задача 2 |
Задача 3 |
Вар № |
|||||||||||||||
|
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
А |
В |
А |
В |
С |
x1 |
x2 |
А |
В |
С |
|||
|
1 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
1 |
2 |
1 |
2 |
1 |
0 |
1 |
2 |
1 |
2 |
1 |
|
|
2 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
2 |
2 |
2 |
2 |
2 |
0 |
1 |
3 |
2 |
2 |
2 |
|
|
3 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
3 |
2 |
3 |
2 |
3 |
0 |
1 |
4 |
3 |
2 |
3 |
|
|
4 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
4 |
2 |
4 |
2 |
5 |
0 |
1 |
5 |
4 |
2 |
4 |
|
|
5 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
5 |
2 |
5 |
2 |
6 |
0 |
1 |
6 |
5 |
2 |
5 |
|
|
6 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
1 |
3 |
1 |
3 |
2 |
0 |
3 |
2 |
1 |
3 |
6 |
|
|
7 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx) |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
2 |
3 |
2 |
3 |
3 |
0 |
3 |
3 |
2 |
3 |
7 |
|
|
8 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
3 |
3 |
3 |
3 |
4 |
0 |
3 |
4 |
3 |
3 |
8 |
|
|
9 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
4 |
3 |
4 |
3 |
5 |
0 |
3 |
5 |
4 |
3 |
9 |
|
|
10 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
5 |
3 |
5 |
3 |
6 |
0 |
3 |
6 |
5 |
3 |
10 |
|
|
11 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
1 |
4 |
1 |
4 |
2 |
0 |
5 |
2 |
1 |
4 |
11 |
|
|
12 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
2 |
4 |
2 |
4 |
3 |
0 |
5 |
3 |
2 |
4 |
12 |
|
|
13 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
3 |
4 |
3 |
4 |
4 |
0 |
5 |
4 |
3 |
4 |
13 |
|
|
14 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
4 |
4 |
4 |
4 |
5 |
0 |
5 |
5 |
4 |
4 |
14 |
|
|
15 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
5 |
4 |
5 |
4 |
6 |
0 |
5 |
6 |
5 |
4 |
15 |
|
|
16 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
2 |
2 |
1 |
16 |
|
|
17 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
2 |
2 |
2 |
2 |
3 |
1 |
2 |
3 |
2 |
2 |
17 |
|
|
18 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
2 |
3 |
2 |
3 |
4 |
1 |
2 |
4 |
2 |
3 |
18 |
|
|
19 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
2 |
4 |
2 |
4 |
5 |
1 |
2 |
5 |
2 |
4 |
19 |
|
|
20 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
2 |
5 |
2 |
5 |
6 |
1 |
2 |
6 |
2 |
5 |
20 |
|
|
21 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
3 |
1 |
3 |
1 |
2 |
1 |
4 |
2 |
3 |
1 |
21 |
|
|
22 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
3 |
2 |
3 |
2 |
3 |
1 |
4 |
3 |
3 |
2 |
22 |
|
|
23 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
3 |
3 |
3 |
3 |
4 |
1 |
4 |
4 |
3 |
3 |
23 |
|
|
24 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
3 |
4 |
3 |
4 |
5 |
1 |
4 |
5 |
3 |
4 |
24 |
|
|
25 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
3 |
5 |
3 |
5 |
6 |
1 |
4 |
6 |
3 |
5 |
25 |
|
|
26 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
4 |
1 |
4 |
1 |
2 |
1 |
5 |
2 |
4 |
1 |
26 |
|
|
27 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
4 |
2 |
4 |
2 |
3 |
1 |
5 |
3 |
4 |
2 |
27 |
|
|
28 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
4 |
3 |
4 |
3 |
4 |
1 |
5 |
4 |
4 |
3 |
28 |
|
|
29 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
4 |
4 |
4 |
4 |
5 |
1 |
5 |
5 |
4 |
4 |
29 |
|
|
30 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
4 |
5 |
4 |
5 |
6 |
1 |
5 |
6 |
4 |
5 |
30 |
|
ВМ 3 ИДЗ 3 - 2012 Интегральное исчисление. Несобственный интеграл Определить интегралы 1 – 4 |
ВМ 3 ИДЗ 4 - 2012 Cтепенные ряды 1. Исследовать сходимость рядов ∞ ∞ ∞ ∞ ∑ (x-A)n /n ; ∑n! (x -B)n; ∑ (x-C)n /n! ; ∑ (x-D)3(n-1)/En-1 ; n=1 n=1 n=1 n=1 2. Разложить функцию f(x) в ряд Тейлора в окрестности точки х0 3. Разложить в ряд Маклорена функцию y(x) |
||||||||||||
|
Вар № |
1 |
2 |
3 |
4 |
A |
B |
C |
D |
E |
f(x) |
xo |
y(x) |
|
|
1 |
∞∫0 e-3x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
5 |
1 |
2 |
4 |
5 |
1 /(1 + x) |
1 |
sin2x |
|
|
2 |
∞∫0 e2x cos3x dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
6 |
2 |
3 |
5 |
6 |
1 /(1 + x) |
2 |
cos2x |
|
|
3 |
∞∫1 [x2(x+1)]-1 dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
1 |
3 |
4 |
6 |
1 |
1 /(1 + x) |
3 |
e 2x |
|
|
4 |
∞∫0 e-3x cosx dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
2 |
4 |
1 |
1 |
2 |
1 /(1 + x) |
4 |
sh2x |
|
|
5 |
∞∫2 {(lnx) /x}dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
3 |
5 |
2 |
2 |
3 |
1 /(1 + 2x) |
1 |
ch2x |
|
|
6 |
∞∫0 x3e-x2 dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
4 |
1 |
3 |
3 |
4 |
1 /(1 + 2x) |
2 |
sin2x |
|
|
7 |
∞∫0 e5x cosx dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
1∫0 {e 1/x / x3 }dx |
5 |
2 |
4 |
4 |
5 |
1 /(1 + 2x) |
3 |
cos2x |
|
|
8 |
∞∫0 e-x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
6 |
3 |
1 |
5 |
6 |
1 /(1 + 2x) |
4 |
e 2x |
|
|
9 |
∞∫0 e2x cos3x dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
1 |
4 |
2 |
6 |
1 |
1 /(1 + 3x) |
1 |
sh2x |
|
|
10 |
∞∫1 [x2(x+1)]-1 dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
2 |
5 |
3 |
1 |
2 |
1 /(1 + 3x) |
2 |
ch2x |
|
|
11 |
∞∫0 e-2x cos5x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
3 |
1 |
4 |
2 |
3 |
1 /(1 + 3x) |
3 |
sin2x |
|
|
12 |
∞∫2 {(lnx) /x}dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
4 |
2 |
1 |
3 |
4 |
1 /(1 + 3x) |
4 |
cos2x |
|
|
13 |
∞∫0 x3e-x2 dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
5 |
3 |
2 |
4 |
5 |
1 /(1 + 4x) |
1 |
e 2x |
|
|
14 |
∞∫0 e5x cosx dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
6 |
4 |
3 |
5 |
6 |
1 /(1 + 4x) |
2 |
sh2x |
|
|
15 |
∞∫0 e-2x dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
2∫0 {1 /(x2 -4x +3)}dx |
1 |
5 |
4 |
6 |
1 |
1 /(1 + 4x) |
3 |
ch2x |
|
|
16 |
∞∫0 e2x cos3x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
1∫0 {e 1/x / x3 }dx |
2 |
1 |
1 |
1 |
2 |
1 /(1 + 4x) |
4 |
sin2x |
|
|
17 |
∞∫1 [x2(x+1)]-1 dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫0 {1 /(x2 -4x +3)}dx |
3 |
2 |
2 |
2 |
3 |
1 /(1 + 5x) |
1 |
cos2x |
|
|
18 |
∞∫0 e-8x cos6x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
4 |
3 |
3 |
3 |
4 |
1 /(1 + 5x) |
2 |
e 2x |
|
|
19 |
∞∫2 {(lnx) /x}dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
5 |
4 |
4 |
4 |
5 |
1 /(1 + 5x) |
3 |
sh2x |
|
|
20 |
∞∫0 x3e-x2 dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
6 |
5 |
1 |
5 |
6 |
1 /(1 + 5x) |
4 |
ch2x |
|
|
21 |
∞∫0 e5x cosx dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
1 |
1 |
2 |
6 |
1 |
1 /(1 + 6x) |
1 |
sin2x |
|
|
22 |
∞∫0 e-4x dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
2 |
2 |
3 |
1 |
2 |
1 /(1 + 6x) |
2 |
cos2x |
|
|
23 |
∞∫0 e2x cos3x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
3 |
3 |
4 |
2 |
3 |
1 /(1 + 6x) |
3 |
e 2x |
|
|
24 |
∞∫1 [x2(x+1)]-1 dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
4 |
4 |
1 |
3 |
4 |
1 /(1 + 6x) |
4 |
sh2x |
|
|
25 |
∞∫0 e-0,3x cos9x dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
5∫3 {x2/√[(x-3)(5–x)]}dx |
5 |
5 |
2 |
4 |
5 |
1 /(1 + 7x) |
1 |
ch2x |
|
|
26 |
∞∫2 {(lnx) /x}dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
1∫0 {1/(1-x2+2√(1-x2)}dx |
6 |
1 |
3 |
5 |
6 |
1 /(1 + 7x) |
2 |
sin2x |
|
|
27 |
∞∫0 x3e-x2 dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
1∫-1 {1 /[(2-x)√(1-x2 )]}dx |
1 |
2 |
4 |
6 |
1 |
1 /(1 + 7x) |
3 |
cos2x |
|
|
28 |
∞∫0 e5x cosx dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
2 |
3 |
1 |
1 |
2 |
1 /(1 + 7x) |
4 |
e 2x |
|
|
29 |
∞∫0 e-7x dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
3 |
4 |
2 |
2 |
3 |
1 /(1 + 8x) |
1 |
sh2x |
|
|
30 |
∞∫0 e-0,1x cosx dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
4 |
5 |
3 |
3 |
4 |
1 /(1 + 8x) |
2 |
ch2x |
РАСШИРЕННЫЙ вариант ИДЗ (для у с е р д н ы х)
|
ВМ 3 2011 Интегральное исчисление. Для выработки навыков интегрирования решить примеры из сб Г.Н.Берман Гл V1 & 1, 2 по силе, но не менее 50% (без сдачи). |
||||||||||||
|
ИДЗ 1 Простейшее Для контроля: |
ИДЗ 2 По частям и возвратные Для контроля: |
|||||||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
Задача 5 |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
Задача 5 |
Вар № |
|
|
1 |
∫ (2x+3)7 dx |
∫ 3√(x-5) dx |
∫ {2x/√(5-4x2)} dx |
∫ {√3/(9x2-3) dx |
∫ e 2x-7 dx |
∫ x3 e 2x dx |
∫ {(x-1)sin2x)} dx |
∫ ln{(2x-5)/ (2x+5)} dx |
∫{sinln(2x-7)}dx |
∫ e3x+2 cos(x-1) dx |
1 |
|
|
2 |
∫ (x+3)7 dx |
∫ 3√(x-7) dx |
∫ {2x/√(3-4x2)} dx |
∫ {√3/(9x2-6) dx |
∫ e 2x-5 dx |
∫ x2 e 3x dx |
∫ {(x+1)cosx)} dx |
∫ ln{(x+7)/ (x-7)} dx |
∫{cosln(3x+5)}dx |
∫ e2x-1 sin(x+2) dx |
2 |
|
|
3 |
∫ (2x+11)7 dx |
∫ 3√(x-3) dx |
∫ {2x/√(7-4x2)} dx |
∫ {√3/(9x2-7) dx |
∫ e 2x-9 dx |
∫ x3 e x dx |
∫ {(x-2)sin2x)} dx |
∫ ln{(2+3x)/ (2-3x)} dx |
∫{sinln(3x+1)}dx |
∫ ex-4 cos(2x) dx |
3 |
|
|
4 |
∫ (2x+7)7 dx |
∫ 3√(x-9) dx |
∫ {2x/√(5-9x2)} dx |
∫ {√3/(4x2-3) dx |
∫ e x-7 dx |
∫ xe 2x+1 dx |
∫ {(x+2)cosx)} dx |
∫ ln{(4x+5)/ (4x-5)} dx |
∫{cosln(2x-3)}dx |
∫ ex+5 sin(3x) dx |
4 |
|
|
5 |
∫ (5x+3)7 dx |
∫ 3√(3x-5) dx |
∫ {2x/√(7-9x2)} dx |
∫ {√3/(x2-5) dx |
∫ e 3x-7 dx |
∫ x3e2x-1 dx |
∫ {(x-3)sinx)} dx |
∫ ln{(3x-7)/ (3x+7)} dx |
∫{sinln(x-1)}dx |
∫ ex+1 cos(x-3) dx |
5 |
|
|
6 |
∫ (4x+3)7 dx |
∫ 3√(7x-5) dx |
∫ {2x/√(5-7x2)} dx |
∫ {√3/(9x2-25) dx |
∫ e 5x-7 dx |
∫ x2e2x-3 dx |
∫ {(x+3)cos2x)} dx |
∫ ln{(2x+3)/ (2x-3)} dx |
∫{cosln(x+1)}dx |
∫ ex-2 sin(x+1) dx |
6 |
|
|
7 |
∫ (7x+3)7 dx |
∫ 3√(2x-7) dx |
∫ {2x/√(4-9x2)} dx |
∫ {√3/(7x2-3) dx |
∫ e 3x-7 dx |
∫ x3e2x+5dx |
∫ {(x-4)sinx)} dx |
∫ ln{(8+3x)/ (8-3x)} dx |
∫{sinln(x-2)}dx |
∫ e3+x cos(x-4) dx |
7 |
|
|
8 |
∫ (5x-3)7 dx |
∫ 3√(3x+5) dx |
∫ {2x/√(7-3x2)} dx |
∫ {√3/(3x2-5) dx |
∫ e 5x-8 dx |
∫ xe 3x-2 dx |
∫ {(x+4)cos2x)} dx |
∫ ln{(7x+3)/ (7x-3)} dx |
∫{cosln(x+2)}dx |
∫ e2-x sin(x+5) dx |
8 |
|
|
9 |
∫ (3x+1)7 dx |
∫ 3√(3x-2) dx |
∫ {2x/√(1-x2)} dx |
∫ {√3/(4x2-1) dx |
∫ e 5x-2 dx |
∫ x3e2x-7 dx |
∫ {(x-5)sinx)} dx |
∫ ln{(9x-2)/ (9x+2)} dx |
∫{sinln(x-3)}dx |
∫ ex-2 cos(x-1) dx |
9 |
|
|
10 |
∫ (7x+3)7 dx |
∫ 3√(2x-5) dx |
∫ {2x/√(3-x2)} dx |
∫ {√3/(5x2-4) dx |
∫ e 3x-1 dx |
∫ x2e2x+1dx |
∫ {(x+5)cos2x)} dx |
∫ ln{(3x+7)/ (3x-7)} dx |
∫{cosln(x+3)}dx |
∫ ex-3 sin(x-2) dx |
10 |
|
|
11 |
∫ (3x+5)7 dx |
∫ 3√(4x-5) dx |
∫ {2x/√(4-3x2)} dx |
∫ {√3/(x2-3) dx |
∫ e 4x-7 dx |
∫ x3e2x+3dx |
∫ {(2x+1)sinx)} dx |
∫ ln{(2-3x)/ (2+3x)} dx |
∫{sinln(x-4)}dx |
∫ ex+2 cos(x+2) dx |
11 |
|
|
12 |
∫ (3x+4)7 dx |
∫ 3√(2x-9) dx |
∫ {2x/√(2-x2)} dx |
∫ {√3/(2x2-1) dx |
∫ e 3x-5 dx |
∫ xe 2x-1 dx |
∫ {(2x-1)cosx)} dx |
∫ ln{(4x-5)/ (4x+5)} dx |
∫{cosln(x+4)}dx |
∫ e2+x sin(x-3) dx |
12 |
|
|
13 |
∫ (4x+5)7 dx |
∫ 3√(7x-8) dx |
∫ {2x/√(3-5x2)} dx |
∫ {√3/(4x2-5) dx |
∫ e 6x-7 dx |
∫ x3e4x-3 dx |
∫ {(2x+2)*sin2x)} dx |
∫ ln{(2x+5)/ (2x-5)} dx |
∫{sinln(x-5)}dx |
∫ ex-3 cos(x+1) dx |
13 |
|
|
14 |
∫ (6x+5)7 dx |
∫ 3√(4x-9) dx |
∫ {2x/√(4-x2)} dx |
∫ {√3/(3x2-1) dx |
∫ e x-8 dx |
∫ x2e3x+5dx |
∫ {(2x-2)cosx)} dx |
∫ ln{(9x+7)/ (9x-7)} dx |
∫{cosln(x+5)}dx |
∫ ex-4 sin(x-4) dx |
14 |
|
|
15 |
∫ (x+9)7 dx |
∫ 3√(3x-7) dx |
∫ {2x/√(2-9x2)} dx |
∫ {√3/(2x2-7) dx |
∫ e 7x-1 dx |
∫ x3e4x-1 dx |
∫ {(2x+3)*sin2x)} dx |
∫ ln{(7+5x)/ (7-5x)} dx |
∫{sinln(x+1)}dx |
∫ ex+7 cos(x+5) dx |
15 |
|
|
16 |
∫ (2x+3)7 dx |
∫ 3√(x-5) dx |
∫ {2x/√(5-4x2)} dx |
∫ {√3/(9x2-3) dx |
∫ e 2x-7 dx |
∫ xe 3x dx |
∫ {(2x-3)cosx)} dx |
∫ ln{(4x+1)/ (4x-1)} dx |
∫{cosln(x-1)}dx |
∫ e2x+1 sin(x-1) dx |
16 |
|
|
17 |
∫ (x+3)7 dx |
∫ 3√(x-7) dx |
∫ {2x/√(3-4x2)} dx |
∫ {√3/(9x2-6) dx |
∫ e 2x-5 dx |
∫ x3e4x-7 dx |
∫ {(2x+4)sinx)} dx |
∫ ln{(2x-1)/ (2x+1)} dx |
∫{sinln(x+2)}dx |
∫ ex+2 cos(x-4) dx |
17 |
|
|
18 |
∫ (2x+11)7 dx |
∫ 3√(x-3) dx |
∫ {2x/√(7-4x2)} dx |
∫ {√3/(9x2-7) dx |
∫ e 2x-9 dx |
∫ x2e3x+5dx |
∫ {(2x-4)cos2x)} dx |
∫ ln{(3x+1)/ (3x-1)} dx |
∫{cosln(x-2)}dx |
∫ e2-x sin(x+7) dx |
18 |
|
|
19 |
∫ (2x+7)7 dx |
∫ 3√(x-9) dx |
∫ {2x/√(5-9x2)} dx |
∫ {√3/(4x2-3) dx |
∫ e x-7 dx |
∫ x3ex-2 dx |
∫ {(2x+5)sinx)} dx |
∫ ln{(2+5x)/ (2-5x)} dx |
∫{sinln(2x)}dx |
∫ ex-6 cos(x-2) dx |
19 |
|
|
20 |
∫ (5x+3)7 dx |
∫ 3√(3x-5) dx |
∫ {2x/√(7-9x2)} dx |
∫ {√3/(x2-5) dx |
∫ e 3x-7 dx |
∫ xe x+4 dx |
∫ {(2x-5)cos2x)} dx |
∫ ln{(4x+5)/ (4x-5)} dx |
∫{cosln(3x)}dx |
∫ e5-x sin(x+3) dx |
20 |
|
|
21 |
∫ (4x+3)7 dx |
∫ 3√(7x-5) dx |
∫ {2x/√(5-7x2)} dx |
∫ {√3/(9x2-25) dx |
∫ e 5x-7 dx |
∫ x3e4x+7dx |
∫ {(3x-1)sin2x)} dx |
∫ ln{(2x-5)/ (2x+5)} dx |
∫{sinln(x+3)}dx |
∫ ex cos(2x-3) dx |
21 |
|
|
22 |
∫ (7x+3)7 dx |
∫ 3√(2x-7) dx |
∫ {2x/√(4-9x2)} dx |
∫ {√3/(7x2-3) dx |
∫ e 3x-7 dx |
∫ x3ex-5 dx |
∫ {(3x+1)cosx)} dx |
∫ ln{(x+7)/ (x-7)} dx |
∫{cosln(x-3)}dx |
∫ ex sin(3x+1) dx |
22 |
|
|
23 |
∫ (5x-3)7 dx |
∫ 3√(3x+5) dx |
∫ {2x/√(7-3x2)} dx |
∫ {√3/(3x2-5) dx |
∫ e 5x-8 dx |
∫ x3e2x+1dx |
∫ {(3x-2)sin2x)} dx |
∫ ln{(2+3x)/ (2-3x)} dx |
∫{sinln(3x)}dx |
∫ e3x cos(x-4) dx |
23 |
|
|
24 |
∫ (3x+1)7 dx |
∫ 3√(3x-2) dx |
∫ {2x/√(1-x2)} dx |
∫ {√3/(4x2-1) dx |
∫ e 5x-2 dx |
∫ x2e4x+3dx |
∫ {(3x+2)cosx)} dx |
∫ ln{(4x+5)/ (4x-5)} dx |
∫{cosln(2x)}dx |
∫ e2x sin(x+5) dx |
24 |
|
|
25 |
∫ (7x+3)7 dx |
∫ 3√(2x-5) dx |
∫ {2x/√(3-x2)} dx |
∫ {√3/(5x2-4) dx |
∫ e 3x-1 dx |
∫ xe 2x-7 dx |
∫ {(3x-3)sin2x)} dx |
∫ ln{(2x-5)/ (2x+5)} dx |
∫{sinln(x+4)}dx |
∫ e3x+1 cosx dx |
25 |
|
|
26 |
∫ (3x+5)7 dx |
∫ 3√(4x-5) dx |
∫ {2x/√(4-3x2)} dx |
∫ {√3/(x2-3) dx |
∫ e 4x-7 dx |
∫ x2e3x+1dx |
∫ {(3x+3)*cos2x)} dx |
∫ ln{(x+7)/ (x-7)} dx |
∫{cosln(x-4)}dx |
∫ e2x sin2x dx |
26 |
|
|
27 |
∫ (3x+4)7 dx |
∫ 3√(2x-9) dx |
∫ {2x/√(2-x2)} dx |
∫ {√3/(2x2-1) dx |
∫ e 3x-5 dx |
∫ xe 4x+3 dx |
∫ {(3x-4)sinx)} dx |
∫ ln{(2+3x)/ (2-3x)} dx |
∫{sinln(x+5)}dx |
∫ e3x cos2x dx |
27 |
|
|
28 |
∫ (4x+5)7 dx |
∫ 3√(7x-8) dx |
∫ {2x/√(3-5x2)} dx |
∫ {√3/(4x2-5) dx |
∫ e 6x-7 dx |
∫ x3e2x-9 dx |
∫ {(3x+4)*cos2x)} dx |
∫ ln{(4x+5)/ (4x-5)} dx |
∫{cosln(x-5)}dx |
∫ e2x sin3x dx |
28 |
|
|
29 |
∫ (6x+5)7 dx |
∫ 3√(4x-9) dx |
∫ {2x/√(4-x2)} dx |
∫ {√3/(3x2-1) dx |
∫ e x-8 dx |
∫{sinln(4x)}dx |
∫ e3x cos5x dx |
29 |
||||
|
30 |
∫ (x+9)7 dx |
∫ 3√(3x-7) dx |
∫ {2x/√(2-9x2)} dx |
∫ {√3/(2x2-7) dx |
∫ e 7x-1 dx |
∫{cosln(4x)}dx |
∫ e2x sin2x dx |
30 |
|
ВМ 3 2011 Интегральное исчисление. Для выработки навыков интегрирования решить примеры из сб Г.Н.Берман Гл V1 & 3 по силе, но не менее 50% (без сдачи). |
|||||||||
|
ИДЗ 5 Разложение дроби на простейшие |
ИДЗ 6 Интегрирование рациональных дробей Для контроля: |
||||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
Задача 1 |
Задача 2 |
Задача 3 |
Вар № |
|
|
1 |
1/(х2 – 13х ) |
(x -2) /(х2 – 4х + 3) |
1 /(х4 - 5х2 - 36) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2+ 4) |
∫{1/(x3+x2-4x-4)} dx |
∫ {(x+3)/(9x2-3)} dx |
∫{(x2+2x+4)/(x4+x2-2)} dx |
1 |
|
|
2 |
2/(х2 + 13х ) |
(x -2) /(х2 – 8х + 15) |
1 /(х4 - 9х2 – 400) |
(х6 + 3х4 - 5х2 + 1) / (х4 - 8х2 + 9) |
∫{2/(x3+2x2-x-2)} dx |
∫ {(x-2)/(4x2+1)} dx |
∫{(x2+3x+6)/(x4+2x2-3)} dx |
2 |
|
|
3 |
3/(х2 – 12х ) |
(x -3) /(х2 – 10х + 24) |
1 /(х4 + 2х2 - 24) |
(х6 - х4 - 7х2 + 40) / (х4 + 10х2 + 2) |
∫{3/(x3+3x2-x-3)} dx |
∫ {(2x+5)/(x2-5)} dx |
∫{(x2+2x+2)/(x4+3x2-4)} dx |
3 |
|
|
4 |
4/(х2 + 12х ) |
(x -3) /(х2 +7х + 10) |
1 /(х4 – 21х2 - 100) |
(х6 + 3х4 - 2х2 + 9) /(х4 - 8х2 + 40) |
∫{4/(x3+4x2+x-6)} dx |
∫ {(4x-7)/(x2+4)} dx |
∫{(x2+3x+2)/(x4+4x2-5)} dx |
4 |
|
|
5 |
5/(х2 + 11х ) |
(x -4) /(х2 – 10х + 24) |
1 /(х4 - 27х2 – 324) |
(х6 + 2х4 - х2 + 14) /(х4 - 28х2 + 49) |
∫{5/(x3+5x2-4x-20)} dx |
∫ {(6x+7)/(x2-3)} dx |
∫{(x2+4x+6)/(x4+x2-2)} dx |
5 |
|
|
6 |
6/(х2 – 11х ) |
(x -3) /(х2 – 10х + 24) |
1 /(х4 + 23х2 - 24) |
(х6 - х4 - х2 + 40) /(х4 + 10х2 + 2) |
∫{6/(x3+6x2+3x-10)} dx |
∫ {(4x+3)/(x2-4)} dx |
∫{(x2+5x+8)/(x4+2x2-3)} dx |
6 |
|
|
7 |
7/(х2 + 10х ) |
(x -1) /(х2 + 3х – 18) |
1 /(х4 - 35х2 - 36) |
(х6 + х4 + 5х2 + 2) /(х4 + 2х2 + 3) |
∫{7/(x3+7x2+7x-15)} dx |
∫ {(8x+7)/(4x2+3)} dx |
∫{(x2+4x+0)/(x4+3x2-4)} dx |
7 |
|
|
8 |
8/(х2 – 10х ) |
(x -2) /(х2 – 4х + 3) |
1 /(х4 + 44х2 – 45) |
(х6 - х4 + 3х2 + 1) /(х4 - 2х2 + 6) |
∫{8/(x3+8x2+11x-20)} dx |
∫ {(2x+13)/(4x2-3)} dx |
∫{(x2+5x+0)/(x4+4x2-5)} dx |
8 |
|
|
9 |
9/(х2 + 9х ) |
(x -4) /(х2 – 2х – 15) |
1 /(х4 – 7х2 - 18) |
(х6 + 2х4 + 4х2 – 1) /(х4 - х2 + 7) |
∫{9/(x3+9x2+8x-60)} dx |
∫ {(2x-9)/(x2+4)} dx |
∫{(x2+6x+8)/(x4+x2-2)} dx |
9 |
|
|
10 |
10/(х2 – 9х ) |
(x +3) /(х2 – 8х + 12) |
1 /(х4 - 7х2 – 144) |
(х6 + 2х4 + 5х2 + 2) /(х4 - х2 + 7) |
∫{10/(x3+10x2+19x-30)} dx |
∫ {(10x+23)/(4x2+9)} dx |
∫{(x2+7x+10)/(x4+2x2-3)} dx |
10 |
|
|
11 |
11/(х2 + 8х ) |
(x -1) /(х2 – 10х + 21) |
1 /(х4 – 48х2 - 49) |
(х6 - 2х4 + 2х2 – 1) /(х4 - 3х2 + 5) |
∫{11/(x3+11x2+38x+40)} dx |
∫ {(x+3)/(x2-16)} dx |
∫{(x2+6x+0)/(x4+3x2-4)} dx |
11 |
|
|
12 |
12/(х2 – 8х ) |
(x -2) /(х2 + х – 42) |
1 /(х4 + 48х2 – 49) |
(х6 + х4 + 3х2 – 2) /(х4 - 2х2 + 6) |
∫{12/(x3+12x2+47x+60)} dx |
∫ {(x+3)/(x2+25)} dx |
∫{(x2+7x+0)/(x4+4x2-5)} dx |
12 |
|
|
13 |
13/(х2 + 7х ) |
(x +5) /(х2 + 3х – 28) |
1 /(х4 + 45х2 -196) |
(х6 + х4 - 5х2 + 10) /(х4 - 6х2 + 25) |
∫{13/(x3+13x2+52x+60)} dx |
∫ {(x+3)/(4x2-9)} dx |
∫{(x2+2x+5)/(x4-3x2-4)} dx |
13 |
|
|
14 |
14/(х2 + 6х ) |
(x -2) /(х2 + 2х – 35) |
1 /(х4 + 35х2 - 36) |
(х6 + х4 - 3х2 + 10) /(х4 + 22х2 + 11) |
∫{14/(x3+14x2+63x+90)} dx |
∫ {(x+3)/(9x2+16)} dx |
∫{(x2+3x+8)/(x4-2x2-8)} dx |
14 |
|
|
15 |
15/(х2 – 7х ) |
(x -9) /(х2 + 2х – 24) |
1 /(х4 - 32х2 – 144) |
(х6 + х4 - х2 + 2) /(х4 + 6х2 – 2) |
∫{15/(x3+15x2+74x+120)} dx |
∫ {(x+3)/(x2-36)} dx |
∫{(x2+2x-1)/(x4-x2-12)} dx |
15 |
|
|
16 |
16/(х2 – 6х ) |
(x +1) /(х2 – 10х + 24) |
1 /(х4 – 33х2 - 108) |
(х6 + 4х4 + х2 + 5) /(х4 + 9х2 + 25) |
∫{16/(x3+16x2+79x+120)} dx |
∫ {(x+3)/(x2+4)} dx |
∫{(x2+3x-1)/(x4+x2-20)} dx |
16 |
|
|
17 |
17/(х2 + 5х ) |
(x -4) /(х2 + 2х – 42) |
1 /(х4 - 47х2 – 98) |
(х6 - 5х4 + 2х2 + 4) /(х4 + 7х2 + 15) |
∫{17/(x3+17x2+92x+160)} dx |
∫ {(x+3)/(x2-25)} dx |
∫{(x2+4x+9)/(x4-3x2-4)} dx |
17 |
|
|
18 |
18/(х2 – 5х ) |
(x -2) /(х2 – 4х + 3) |
1 /(х4 - 45х2 - 196) |
(х6 - х4 + 3х2 + 4) /(х4 - 6х2 + 2) |
∫{18/(x3+18x2+105x+200)} dx |
∫ {(8x+23)/(16x2+9)} dx |
∫{(x2+5x+12)/(x4-2x2-8)} dx |
18 |
|
|
19 |
19/(х2 + 4х ) |
(x -4) /(х2 – 14х + 48) |
1 /(х4 - 63х2 – 64) |
(х6 + х4 + 3х2 – 2) /(х4 + х2 – 5) |
∫{19/(x3+19x2+118x+240)} dx |
∫ {(2x+13)/(x2-49)} dx |
∫{(x2+4x-5)/(x4-x2-12)} dx |
19 |
|
|
20 |
20/(х2 – 4х ) |
(x +5) /(х2 + 2х - 63) |
1 /(х4 - 77х2 - 324) |
(х6 - х4 + 3х2 + 6) /(х4 + 10х2 + 6) |
∫{20/(x3+20x2+131x+280)} dx |
∫ {(2x+8)/(x2+1)} dx |
∫{(x2+5x-5)/(x4+x2-20)} dx |
20 |
|
|
21 |
21/(х2 + 3х ) |
(x -7) /(х2 – 18х + 80) |
1 /(х4 - 97х2 – 300) |
(х6 – 7х4 - х2 + 9) /(х4 - 4х2 + 20) |
∫{21/(x3+21x2+146x+336)} dx |
∫ {(2x+6)/(x2-2)} dx |
∫{(x2+6x+13)/(x4-3x2-4)} dx |
21 |
|
|
22 |
22/(х2 – 3х ) |
(x -7) /(х2 + х – 90) |
1 /(х4 - 99х2 – 100) |
(х6 - 2х4 + 6х2 + 5) /(х4 - х2 + 3) |
∫{22/(x3+22x2+161x+392)} dx |
∫ {(6x-4)/(x2+9)} dx |
∫{(x2+7x+15)/(x4-2x2-8)} dx |
22 |
|
|
23 |
23/(х2 + 2х ) |
(x -3) /(х2 – 15х + 56) |
1 /(х4 - 60х2 - 256) |
(х6 + 2х4 + 4х2 – 6) /(х4 + 14х2 – 7) |
∫{23/(x3+23x2+176x+448)} dx |
∫ {(4x-2)/(x2-7)} dx |
∫{(x2+6x-11)/(x4-x2-12)} dx |
23 |
|
|
24 |
24/(х2 + х ) |
(x -2) /(х2 – х – 72) |
1 /(х4 - 78х2 – 243) |
(х6 + х4 + 3х2 + 2) /(х4 + 4х2 – 2) |
∫{24/(x3+24x2+191x+504)} dx |
∫ {(2x-10)/(x2+16)} dx |
∫{(x2+7x-13)/(x4+x2-20)} dx |
24 |
|
|
25 |
25/(х2 – х ) |
(x -4) /(х2 – 16х + 63) |
1 /(х4 - 72х2 – 729) |
(х6 - 3х4 + х2 + 7) /(х4 + 2х2 + 12) |
∫{25/(x3+25x2+208x+576)} dx |
∫ {(8x+16)/(4x2+25)} dx |
∫{(x2+2x+7)/(x4-8x2-9)} dx |
25 |
|
|
26 |
26/(х2 – 5х ) |
(x -2) /(х2 – 4х + 3) |
1 /(х4 - 9х2 – 400) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2 + 4) |
∫{26/(x3+26x2+225x+648)} dx |
∫ {(4x-6)/(4x2+5)} dx |
∫{(x2+3x+11)/(x4-7x2-27)} dx |
26 |
|
|
27 |
1 /(х4 - 5х2 - 36) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2 + 4) |
∫{27/(x3+27x2+242x+720)} dx |
∫ {(2x-12)/(9x2+4)} dx |
∫{(x2+2x-3)/(x4-6x2-36)} dx |
27 |
|||
|
28 |
1 /(х4 - 9х2 – 400) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2 + 4) |
∫{28/(x3+28x2+261x+810)} dx |
∫ {(4x+10)/(9x2+16)} dx |
∫{(x2+3x-5)/(x4-5x2-45)} dx |
28 |
|||
|
29 |
1 /(х4 - 5х2 - 36) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2 + 4) |
29 |
||||||
|
30 |
1 /(х4 - 9х2 – 400) |
(х6 - 5х4 + 7х2 + 14) /(х4 - 12х2 + 4) |
30 |
|
ВМ 3 2011 Интегральное исчисление. Для выработки навыков интегрирования решить примеры из сб Г.Н.Берман Гл V1 & 3 по силе, но не менее 50% (без сдачи). Тригонометрические функции |
||||||||
|
ИДЗ 3 |
ИДЗ 4 |
|||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 1 |
Задача 2 |
Задача 3 |
Вар № |
|
|
1 |
∫Аsin3 x cos2x dx |
∫ tg4x dx |
∫(sinx + cosx)2dx |
∫ {sin2x/ cos3x} dx |
∫ {B/(1-3sinx+cosx)} dx |
∫{[3 - cos2x]/[(cosx + sinx)2}dx |
1 |
|
|
2 |
∫2sin3 x cos6x dx |
∫ сtg4x dx |
∫(sinx - cosx)2dx |
∫ {2cos2x/ sin3x } dx |
∫ {2/(2-3sinx-cosx)} dx |
∫{[3 + sin2x]/[(cosx + sinx)2}dx |
2 |
|
|
3 |
∫3sin4 x cos2x dx |
∫ tg5x dx |
∫(sinx + 3cosx)2dx |
∫ {4sin2x/ cosx } dx |
∫ {3/(3+3sinx+cosx)} dx |
∫{[3 - sin2x]/[(cosx + sinx)2}dx |
3 |
|
|
4 |
∫4sin2x cos4x dx |
∫ сtg5x dx |
∫(sinx – 3cosx)2dx |
∫ {5cos2x/ sinx } dx |
∫ {4/(4+3sinx-cosx)} dx |
∫{[3 - cos2x]/[(cosx - sinx)2}dx |
4 |
|
|
5 |
∫5sin2 x cos2x dx |
∫ tg6x dx |
∫(sinx + 5cosx)2dx |
∫ {6sin4x/ cos2x } dx |
∫ {5/(5-sinx+3cosx)} dx |
∫{[3 - sin2x]/[(cosx - sinx)2}dx |
5 |
|
|
6 |
∫6sin2 x cos3x dx |
∫ сtg6x dx |
∫(sinx – 5cosx)2dx |
∫ {7cos4x/ sin2x } dx |
∫ {6/(5-sinx-3cosx)} dx |
∫{[3 - cos2x]/[(cosx - sinx)2}dx |
6 |
|
|
7 |
∫7sin5 x cos2x dx |
∫ 7tg3x dx |
∫(sinx + 7cosx)2dx |
∫ {8sin6x/ cos2x } dx |
∫ {7/(4+sinx+3cosx)} dx |
∫{[4 - cos2x]/[(cosx + sinx)2}dx |
7 |
|
|
8 |
∫8sin2 x cos5x dx |
∫ 8сtg2x dx |
∫(sinx – 7cosx)2dx |
∫ {9cos6x/ sin2x } dx |
∫ {8/(3+sinx-3cosx)} dx |
∫{[4 + sin2x]/[(cosx + sinx)2}dx |
8 |
|
|
9 |
∫9sin3 x cos4x dx |
∫ 9tg4x dx |
∫(sinx + 9cosx)2dx |
∫ {10sin4x/ cosx } dx |
∫ {9/(2-2sinx+cosx)} dx |
∫{[4 - sin2x]/[(cosx + sinx)2}dx |
9 |
|
|
10 |
∫10sin4 x cos3x dx |
∫ 10сtg2x dx |
∫(sinx - 9cosx)2dx |
∫ {11cos4x/ sinx } dx |
∫ {10/(1-2sinx-cosx)} dx |
∫{[4 - cos2x]/[(cosx - sinx)2}dx |
10 |
|
|
11 |
∫11sin3 x cos2x dx |
∫ 11tg4x dx |
∫(2sinx + 2cosx)2dx |
∫ {12sin4x/ cos3x } dx |
∫ {11/(1+2sinx+cosx)} dx |
∫{[4 - sin2x]/[(cosx - sinx)2}dx |
11 |
|
|
12 |
∫12sin3 x cos6x dx |
∫ 12сtg4x dx |
∫(2sinx - 2cosx)2dx |
∫ {13cos4x/ sin3x } dx |
∫ {12/(2+2sinx-cosx)} dx |
∫{[4 - cos2x]/[(cosx - sinx)2}dx |
12 |
|
|
13 |
∫13sin2 x cos4x dx |
∫ tg5x dx |
∫(2sinx + 4cosx)2dx |
∫ {14sin3x/ cos5x } dx |
∫ {13/(3-sinx+2cosx)} dx |
∫{[5 - cos2x]/[(cosx + sinx)2}dx |
13 |
|
|
14 |
∫14sin4 x cos2x dx |
∫ сtg5x dx |
∫(2sinx – 4cosx)2dx |
∫ {15cos3x/ sin5x } dx |
∫ {14/(4-sinx-2cosx)} dx |
∫{[5 + sin2x]/[(cosx + sinx)2}dx |
14 |
|
|
15 |
∫15sin2 x cos2x dx |
∫ tg6x dx |
∫(2sinx + 6cosx)2dx |
∫ {16sin3x/ cos3x } dx |
∫ {15/(5+sinx+2cosx)} dx |
∫{[5 - sin2x]/[(cosx + sinx)2}dx |
15 |
|
|
16 |
∫16sin2 x cos3x dx |
∫ сtg6x dx |
∫(2sinx – 6cosx)2dx |
∫ {17cos3x/ sin3x } dx |
∫ {16/(5+sinx-2cosx)} dx |
∫{[5 - cos2x]/[(cosx - sinx)2}dx |
16 |
|
|
17 |
∫17sin5 x cos2x dx |
∫ 17tg3x dx |
∫(2sinx + 8cosx)2dx |
∫ {18sin2x/ cos3x } dx |
∫ {17/(4-sinx+cosx)} dx |
∫{[5 - sin2x]/[(cosx - sinx)2}dx |
17 |
|
|
18 |
∫18sin2 x cos5x dx |
∫ 18сtg3x dx |
∫(2sinx - 8cosx)2dx |
∫ {19cos2x/ sin3x } dx |
∫ {18/(3-sinx-cosx)} dx |
∫{[5 - cos2x]/[(cosx - sinx)2}dx |
18 |
|
|
19 |
∫19sin3 x cos4x dx |
∫ 19tg2x dx |
∫(sinx + 3cosx)2dx |
∫ {29sin2x/ cosx } dx |
∫ {19/(2+2sinx+2cosx)} dx |
∫{[6 - cos2x]/[(cosx + sinx)2}dx |
19 |
|
|
20 |
∫20sin4 x cos3x dx |
∫ 20сtg2x dx |
∫(sinx – 3cosx)2dx |
∫ {20cos2x/ sinx } dx |
∫ {20/(1+2sinx-2cosx)} dx |
∫{[6 + sin2x]/[(cosx + sinx)2}dx |
20 |
|
|
21 |
∫21sin6 x cos3x dx |
∫ 21tg4x dx |
∫(sinx + 5cosx)2dx |
∫ {21sin4x/ cos2x } dx |
∫ {21/(1-4sinx+cosx)} dx |
∫{[6 - sin2x]/[(cosx + sinx)2}dx |
21 |
|
|
22 |
∫22sin4 x cos2x dx |
∫ 22сtg4x dx |
∫(sinx – 5cosx)2dx |
∫ {22cos4x/ sin2x } dx |
∫ {22/(2-4sinx-cosx)} dx |
∫{[6 - cos2x]/[(cosx - sinx)2}dx |
22 |
|
|
23 |
∫23sin2 x cos4x dx |
∫ 23tg5x dx |
∫(sinx + 7cosx)2dx |
∫ {23sin6x/ cos2x } dx |
∫ {23/(3+4sinx+cosx)} dx |
∫{[6 - sin2x]/[(cosx - sinx)2}dx |
23 |
|
|
24 |
∫24sin2 x cos2x dx |
∫ 24сtg5x dx |
∫(sinx – 7cosx)2dx |
∫ {24cos6x/ sin2x } dx |
∫ {24/(4+4sinx-cosx)} dx |
∫{[6 - cos2x]/[(cosx - sinx)2}dx |
24 |
|
|
25 |
∫25sin2 x cos3x dx |
∫ 25tg6x dx |
∫(sinx + 9cosx)2dx |
∫ {25sin4x/ cosx } dx |
∫ {25/(5-sinx+4cosx)} dx |
∫{[7 - cos2x]/[(cosx + sinx)2}dx |
25 |
|
|
26 |
∫26sin5 x cos2x dx |
∫ 26сtg6x dx |
∫(sinx - 9cosx)2dx |
∫ {26cos4x/ sinx } dx |
∫ {26/(5-sinx-4cosx)} dx |
∫{[7 + sin2x]/[(cosx + sinx)2}dx |
26 |
|
|
27 |
∫27sin2 x cos5x dx |
∫ 27tg3x dx |
∫(2sinx + 2cosx)2dx |
∫ {27sin4x/ cos3x } dx |
∫ {27/(4+sinx+4cosx)} dx |
∫{[7 - sin2x]/[(cosx + sinx)2}dx |
27 |
|
|
28 |
∫28sin3 x cos4x dx |
∫ 28сtg3x dx |
∫(2sinx - 2cosx)2dx |
∫ {28cos4x/ sin3x } dx |
∫ {28/(3+sinx-4cosx)} dx |
∫{[7 - cos2x]/[(cosx - sinx)2}dx |
28 |
|
|
29 |
∫29sin4 x cos3x dx |
∫ 29tg2x dx |
∫(2sinx + 4cosx)2dx |
∫ {13sin3x/ cos5x } dx |
∫ {29/(2-3sinx+4cosx)} dx |
∫{[7 - sin2x]/[(cosx - sinx)2}dx |
29 |
|
|
30 |
∫30sin3 x cos6x dx |
∫ 30сtg2x dx |
∫(2sinx – 4cosx)2dx |
∫ {30cos3x/ sin5x } dx |
∫ {30/(1-3sinx-4cosx)} dx |
∫{[7 - cos2x]/[(cosx - sinx)2}dx |
30 |
|
ВМ 3 2011 Интегральное исчисление. Для выработки навыков интегрирования решить примеры из сб Г.Н.Берман Гл V1 & 2, 3 по силе, но не менее 50% (без сдачи).
|
||||||||
|
ИДЗ 7 Простейшие иррациональные функции |
ИДЗ 8 Трансцедентные и гиперболические функции |
|||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 1 |
Задача 2 |
Задача 3 |
Вар № |
|
|
1 |
∫ {1/(6+√(2x-1))}dx |
∫{[(3√x2 )+2x+1]/√(2x)} dx |
∫ {x/√(x2 +2x+10)} dx |
∫ {1/(6+ e2x)}dx |
∫{(ex +1)/(9+e2x)} dx |
∫ {1/ (3 +shx)} dx |
1 |
|
|
2 |
∫ {1/(5-√(x+2))}dx |
∫{[(3√x2 )+3x-2]/√(3x)} dx |
∫ {1/(х+1)√(x2 +2x+2)} dx |
∫ {1/(5- ex )}dx |
∫{( ex -2)/√(4+e2x )} dx |
∫ {1/ (2 +chx)} dx |
2 |
|
|
3 |
∫ {1/(4+√(4x-3))}dx |
∫{[(3√x2 )-4x+3]/√(5x)} dx |
∫ {2x/√(x2 -2x+10)} dx |
∫ {1/(4+ e4x )}dx |
∫{( ex +3)/(3+e2x )} dx |
∫ {1/ (1 +shx)} dx |
3 |
|
|
4 |
∫ {1/(3-√(3x+4))}dx |
∫{[(3√x2 )-5x-4]/√(7x)} dx |
∫ {2/(х+1)√(x2 +2x)} dx |
∫ {1/(3- e3x )}dx |
∫{( ex -4)/√( 2+e2x )} dx |
∫ {1/ (3 +chx)} dx |
4 |
|
|
5 |
∫ {1/(2+√(7x-5))}dx |
∫{[(3√x2 )+6x+5]/√x} dx |
∫ {4/3(х+1)√(3-x2 -2x)} dx |
∫ {1/(2+ e7x )}dx |
∫{( ex +5)/( 1+e2x)} dx |
∫ {1/ (2 +shx)} dx |
5 |
|
|
6 |
∫ {1/(1-√(5x+6))}dx |
∫{[(3√x2 )+7x-6]/√(2x)} dx |
∫ {x/√(x2 +4x+13)} dx |
∫ {1/(1- e5x )}dx |
∫{( ex -6)/√( 1+e2x )} dx |
∫ {1/ (1 +chx)} dx |
6 |
|
|
7 |
∫ {1/(1+√(5x-7))}dx |
∫{[(3√x2 )-8x+7]/√(3x)} dx |
∫ {1/(х-1)√(x2 -2x+2)} dx |
∫ {1/(1+ e5x )}dx |
∫{( ex +7)/√( 2+e2x )} dx |
∫ {1/ (3 +sh2x)} dx |
7 |
|
|
8 |
∫ {1/(2-√(7x+8))}dx |
∫{[(3√x2 )-9x-8]/√(5x)} dx |
∫ {2x/√(x2 -4x+13)} dx |
∫ {1/(2- e7x )}dx |
∫{( ex -8)/√( 3+e2x )} dx |
∫ {1/ (2 +ch2x)} dx |
8 |
|
|
9 |
∫ {1/(3+√(4x-9))}dx |
∫{[(3√x2 )+ x+9]/√(7x)} dx |
∫ {2/(х-1)√(x2 -2x)} dx |
∫ {1/(3+ e4x )}dx |
∫{( ex +9)/√( 4+e2x )} dx |
∫ {1/ (1 +sh2x)} dx |
9 |
|
|
10 |
∫ {1/(4-√(x+9))}dx |
∫{[(3√x2 )+9x-10]/√x } dx |
∫ {4/3(х-1)√(2х -x2 )} dx |
∫ {1/(4- ex )}dx |
∫{( ex -10)/( 9+e2x) } dx |
∫ {1/ (3 +ch2x)} dx |
10 |
|
|
11 |
∫ {1/(6-√(3x-8))}dx |
∫{[(3√x2 )-8x+11]/√(2x)} dx |
∫ {x/√(x2 +2x-8)} dx |
∫ {1/(6- e3x )}dx |
∫{( ex +11)/√( 9+e2x )} dx |
∫ {1/ (2 +sh2x)} dx |
11 |
|
|
12 |
∫ {1/(5+√(2x+7))}dx |
∫{[(3√x2 )-7x-12]/√(3x)} dx |
∫ {1/(х+2)√(x2 +4x+5)} dx |
∫ {1/(5+ e2x )}dx |
∫{( ex -12)/√( 4+e2x )} dx |
∫ {1/ (1 +ch2x)} dx |
12 |
|
|
13 |
∫ {1/(6-√(5x-6))}dx |
∫{[(3√x2 )+6x+13]/√(5x)} dx |
∫ {2x/√(x2 -2x-8)} dx |
∫ {1/(6- e5x )}dx |
∫{( ex +13)/√( 3+e2x )} dx |
∫ {1/ (3 +sh3x)} dx |
13 |
|
|
14 |
∫ {1/(7+√(2x+5))}dx |
∫{[(3√x2 )+5x-14]/√(7x)} dx |
∫ {2/(х+2)√(x2 +4x+3)} dx |
∫ {1/(7+ e2x )}dx |
∫{( ex -14)/√( 2+e2x )} dx |
∫ {1/ (2 +ch3x)} dx |
14 |
|
|
15 |
∫ {1/(8-√(x-4))}dx |
∫{[(3√x2 )-4x+15]/√x } dx |
∫ {4/3(х+2)√(5-x2 -4x)} dx |
∫ {1/(8- ex )}dx |
∫{( ex +15)/( 1+e2x) } dx |
∫ {1/ (1 +sh3x)} dx |
15 |
|
|
16 |
∫ {1/(9+√(2x+3))}dx |
∫{[(3√x2 )-3x-15]/√(2x)} dx |
∫ {x/√(8-x2 -2x)} dx |
∫ {1/(9+ e2x )}dx |
∫{( ex -15)/√( 1+e2x )} dx |
∫ {1/ (3 +ch3x)} dx |
16 |
|
|
17 |
∫ {1/(9-√(x-2))}dx |
∫{[(3√x2 )+2x+14]/√(3x)} dx |
∫ {1/(х-2)√(x2 -4x+5)} dx |
∫ {1/(9- ex )}dx |
∫{( ex +14)/√( 2+e2x )} dx |
∫ {1/ (2 +sh3x)} dx |
17 |
|
|
18 |
∫ {1/(8+√(3x+1))}dx |
∫{[(3√x2 )+ x-13]/√(5x)} dx |
∫ {2x/√(8-x2 +2x)} dx |
∫ {1/(8+ e3x )}dx |
∫{( ex -13)/√( 3+e2x )} dx |
∫ {1/ (1 +ch3x)} dx |
18 |
|
|
19 |
∫ {1/(7-√(5x-1))}dx |
∫{[(3√x2 )- x+12]/√(7x)} dx |
∫ {2/(х-2)√(x2 -4x+3)} dx |
∫ {1/(7- e5x )}dx |
∫{( ex +12)/√(4+e2x )} dx |
∫ {1/ (3 - shx)} dx |
19 |
|
|
20 |
∫ {1/(1+√(3x+1))}dx |
∫{[(3√x2 )- 2x-11]/√x } dx |
∫ {4/3(х-2)√(5-x2 +4x)} dx |
∫ {1/(1+ e3x )}dx |
∫{( ex -11)/( 9+e2x) } dx |
∫ {1/ (2 - chx)} dx |
20 |
|
|
21 |
∫ {1/(2-√(7x-2))}dx |
∫{[(3√x2 )+3x+10]/√(2x)} dx |
∫ {x/√(x2 +4x-5)} dx |
∫ {1/(2- e7x )}dx |
∫{( ex +10)/√(9+e2x )} dx |
∫ {1/ (1 - shx)} dx |
21 |
|
|
22 |
∫ {1/(3+√(5x+3))}dx |
∫{[(3√x2 )+4x-9]/√(3x)} dx |
∫ {1/(х+1)√(x2 +2x+5)} dx |
∫ {1/(3+ e5x )}dx |
∫{( ex -9)/√(3+e2x )} dx |
∫ {1/ (3 - chx)} dx |
22 |
|
|
23 |
∫ {1/(4-√(3x-4))}dx |
∫{[(3√x2 )-5x+8]/√(5x)} dx |
∫ {2x/√(x2 -4x-5)} dx |
∫ {1/(4- e3x )}dx |
∫{( ex +8)/√(4+e2x )} dx |
∫ {1/ (2 - shx)} dx |
23 |
|
|
24 |
∫ {1/(5+√(x+5))}dx |
∫{[(3√x2 )-6x-7]/√(7x)} dx |
∫ {2/(х+1)√(x2 +2x+3)} dx |
∫ {1/(5+ ex )}dx |
∫{( ex -7)/√(2+e2x )} dx |
∫ {1/ (1 - chx)} dx |
24 |
|
|
25 |
∫ {1/(5-√(5x-6))}dx |
∫{[(3√x2 )+7x+6]/√x } dx |
∫ {4/3(х+1)√(3-x2 -2x)} dx |
∫ {1/(5- e5x )}dx |
∫{( ex +6)/ 1+e2x )} dx |
∫ {1/ (3 - sh2x)} dx |
25 |
|
|
26 |
∫ {1/(4+√(3x+7))}dx |
∫{[(3√x2 )+8x-5]/√(2x)} dx |
∫ {x/√(5-x2 -4x)} dx |
∫ {1/(4+ e3x )}dx |
∫{( ex -5)/√(1+e2x )} dx |
∫ {1/ (2 - ch2x)} dx |
26 |
|
|
27 |
∫ {1/(3-√(5x-8))}dx |
∫{[(3√x2 )-9x+4]/√(3x)} dx |
∫ {1/(х-1)√(x2 -2x+5)} dx |
∫ {1/(3- e5x )}dx |
∫{( ex +4)/√(2+e2x )} dx |
∫ {1/ (1 - sh2x)} dx |
27 |
|
|
28 |
∫ {1/(2+√(4x+9))}dx |
∫{[(3√x2 )- x-3]/√(5x)} dx |
∫ {4x/√(5-x2 +4x)} dx |
∫ {1/(2+ e4x )}dx |
∫{( ex -3)/√(3+e2x )} dx |
∫ {1/ (3 - ch2x)} dx |
28 |
|
|
29 |
29 |
|
ВМ 3 2011 Определенный Интеграл. |
||||||||||||||||||||||||
|
ИДЗ 9 “O” Вычисление ОИ и нахождение площадей x2 1. В задачах 1 – 4 вычислить определенный интеграл ∫ f(x) dx x1 2. В задачах 5 и 6 вычислить площадь плоской фигуры, ограниченной линиями а) Х2 / А2 + У2 / В2 = 1 ; б) У = А – В Х3, Х=0 и У=0 |
ИДЗ 10 Вычисление объема тела вращения, площади поверхности и длины дуги плоской кривой 1. В задаче 1 вычислить объем тела вращения Х2 / А2 + У2 / В2 = 1 вокруг оси Ох 2. В задаче 2 вычислить площадь поверхности тела вращения У= Х3 / С вокруг оси Ох при Х1 <X < X2 3. В задаче 3 вычислить длину дуги плоской кривой { X = t6 / A; Y = B – t4 / C } между точками пересечения ее с осями координат. |
|||||||||||||||||||||||
|
Вар № |
Задача 1 |
Задача 2 |
Задача 3 |
Задача 4 |
З 5, 6 |
Задача 1 |
Задача 2 |
Задача 3 |
Вар № |
|||||||||||||||
|
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
f(x) |
x1 |
x2 |
А |
В |
А |
В |
С |
x1 |
x2 |
А |
В |
С |
|||
|
1 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
1 |
2 |
1 |
2 |
1 |
0 |
1 |
2 |
1 |
2 |
1 |
|
|
2 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
2 |
2 |
2 |
2 |
2 |
0 |
1 |
3 |
2 |
2 |
2 |
|
|
3 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
3 |
2 |
3 |
2 |
3 |
0 |
1 |
4 |
3 |
2 |
3 |
|
|
4 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
4 |
2 |
4 |
2 |
5 |
0 |
1 |
5 |
4 |
2 |
4 |
|
|
5 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
5 |
2 |
5 |
2 |
6 |
0 |
1 |
6 |
5 |
2 |
5 |
|
|
6 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
1 |
3 |
1 |
3 |
2 |
0 |
3 |
2 |
1 |
3 |
6 |
|
|
7 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx) |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
2 |
3 |
2 |
3 |
3 |
0 |
3 |
3 |
2 |
3 |
7 |
|
|
8 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
3 |
3 |
3 |
3 |
4 |
0 |
3 |
4 |
3 |
3 |
8 |
|
|
9 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
4 |
3 |
4 |
3 |
5 |
0 |
3 |
5 |
4 |
3 |
9 |
|
|
10 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
5 |
3 |
5 |
3 |
6 |
0 |
3 |
6 |
5 |
3 |
10 |
|
|
11 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
1 |
4 |
1 |
4 |
2 |
0 |
5 |
2 |
1 |
4 |
11 |
|
|
12 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
2 |
4 |
2 |
4 |
3 |
0 |
5 |
3 |
2 |
4 |
12 |
|
|
13 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
3 |
4 |
3 |
4 |
4 |
0 |
5 |
4 |
3 |
4 |
13 |
|
|
14 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
4 |
4 |
4 |
4 |
5 |
0 |
5 |
5 |
4 |
4 |
14 |
|
|
15 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
5 |
4 |
5 |
4 |
6 |
0 |
5 |
6 |
5 |
4 |
15 |
|
|
16 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
2 |
2 |
1 |
16 |
|
|
17 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
2 |
2 |
2 |
2 |
3 |
1 |
2 |
3 |
2 |
2 |
17 |
|
|
18 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
2 |
3 |
2 |
3 |
4 |
1 |
2 |
4 |
2 |
3 |
18 |
|
|
19 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
2 |
4 |
2 |
4 |
5 |
1 |
2 |
5 |
2 |
4 |
19 |
|
|
20 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
2 |
5 |
2 |
5 |
6 |
1 |
2 |
6 |
2 |
5 |
20 |
|
|
21 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
3 |
1 |
3 |
1 |
2 |
1 |
4 |
2 |
3 |
1 |
21 |
|
|
22 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
3 |
2 |
3 |
2 |
3 |
1 |
4 |
3 |
3 |
2 |
22 |
|
|
23 |
√(3-x2 ) |
0 |
√3 |
(х+1) е –2х |
-1 |
0 |
1 / (2+cosx |
0 |
п/2 |
(x-1)2 /(x2 + 3x+4) |
-1,5 |
2 |
3 |
3 |
3 |
3 |
4 |
1 |
4 |
4 |
3 |
3 |
23 |
|
|
24 |
(x2 ) √(9 - x2 ) |
-3 |
3 |
1/ ex (3+е –х ) |
0 |
ln2 |
sinх /(1-cosx)3 |
п/2 |
п |
(3x-2) /(x2 - 4x+5) |
2 |
3 |
3 |
4 |
3 |
4 |
5 |
1 |
4 |
5 |
3 |
4 |
24 |
|
|
25 |
(x3 ) √(1+x2 ) |
0 |
√3 |
х е –2х |
- ½ |
0 |
sin2х / cos3x |
п/6 |
п/3 |
1 /(x2 + 3x - 10) |
4 |
7 |
3 |
5 |
3 |
5 |
6 |
1 |
4 |
6 |
3 |
5 |
25 |
|
|
26 |
12x5 /√(x6+1) |
0 |
12√3 |
e 1/x /x2 |
½ |
1 |
1/sinx |
п/3 |
п/2 |
1/(x2+2x+3) |
-1 |
1 |
4 |
1 |
4 |
1 |
2 |
1 |
5 |
2 |
4 |
1 |
26 |
|
|
27 |
√(x+1) |
3 |
8 |
3х2 (1+е х3 ) |
0 |
1 |
1/sin3x |
п/3 |
п/2 |
1/(x2+4x+5) |
0 |
1 |
4 |
2 |
4 |
2 |
3 |
1 |
5 |
3 |
4 |
2 |
27 |
|
|
28 |
(x3 ) √(9+x2 ) |
0 |
4 |
х2 е –x/2 |
-2 |
0 |
sin2x cos2x |
0 |
п/2 |
x3/(x2 - 3x+2) |
7 |
10 |
4 |
3 |
4 |
3 |
4 |
1 |
5 |
4 |
4 |
3 |
28 |
|
|
29 |
(x2 ) √(4-x2 ) |
0 |
2 |
х е –3х |
- 1/3 |
-2/3 |
0,5sin2x |
-п |
п |
x3/(x2+ x+ 1) |
-0,5 |
1 |
4 |
4 |
4 |
4 |
5 |
1 |
5 |
5 |
4 |
4 |
29 |
|
|
30 |
√(4-x2 ) |
0 |
1 |
(х-2) е –3х |
-3 |
0 |
cos3x / 3√sinx |
-п/2 |
п/4 |
x /(x4- 4x2+3) |
4 |
5 |
4 |
5 |
4 |
5 |
6 |
1 |
5 |
6 |
4 |
5 |
30 |
|
ВМ 3 2012 ИДЗ 3 Интегральное исчисление. Несобственный интеграл Определить интегралы 1 – 4 |
||||||||||
|
Вар № |
1 |
2 |
3 |
4 |
1 |
2 |
3 |
4 |
Вар № |
|
|
1 |
∞∫0 e-3x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
∞∫0 e2x cos3x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
1∫0 {e 1/x / x3 }dx |
16 |
|
|
2 |
∞∫0 e2x cos3x dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
∞∫1 [x2(x+1)]-1 dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫0 {1 /(x2 -4x +3)}dx |
17 |
|
|
3 |
∞∫1 [x2(x+1)]-1 dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
∞∫0 e-8x cos6x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
18 |
|
|
4 |
∞∫0 e-3x cosx dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
∞∫2 {(lnx) /x}dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
19 |
|
|
5 |
∞∫2 {(lnx) /x}dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
∞∫0 x3e-x2 dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
20 |
|
|
6 |
∞∫0 x3e-x2 dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
∞∫0 e5x cosx dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
21 |
|
|
7 |
∞∫0 e5x cosx dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
1∫0 {e 1/x / x3 }dx |
∞∫0 e-4x dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
22 |
|
|
8 |
∞∫0 e-x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
∞∫0 e2x cos3x dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
23 |
|
|
9 |
∞∫0 e2x cos3x dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
∞∫1 [x2(x+1)]-1 dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
24 |
|
|
10 |
∞∫1 [x2(x+1)]-1 dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
∞∫0 e-0,3x cos9x dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
5∫3 {x2/√[(x-3)(5–x)]}dx |
25 |
|
|
11 |
∞∫0 e-2x cos5x dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
2∫0 {1 /(x2 -4x +3)}dx |
∞∫2 {(lnx) /x}dx |
0∫-∞ ex sinx dx |
∞∫-∞ {2x /(x2 +1)}dx |
1∫0 {1/(1-x2+2√(1-x2)}dx |
26 |
|
|
12 |
∞∫2 {(lnx) /x}dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
2∫1 {x /√(x – 1)}dx |
∞∫0 x3e-x2 dx |
1∫-∞ [x2 +1] -2 dx |
∞∫-∞ [x√(1+x2)] -1dx |
1∫-1 {1 /[(2-x)√(1-x2 )]}dx |
27 |
|
|
13 |
∞∫0 x3e-x2 dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫0 x lnx dx |
∞∫0 e5x cosx dx |
-2∫-∞ x(x+1) -3 dx |
∞∫-∞ {1/(x2 +2x+2)} dx |
1∫-1 {(x+1) / 5√x3 }dx |
28 |
|
|
14 |
∞∫0 e5x cosx dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1/e∫0 {1 /(x ln2 x)}dx |
∞∫0 e-7x dx |
0∫-∞ {1/(x2 +2x+2)} dx |
∞∫-∞ [x2 +1] -2 dx |
1∫-1 {ln(2+3√x) / 3√x}dx |
29 |
|
|
15 |
∞∫0 e-2x dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
2∫0 {1 /(x2 -4x +3)}dx |
∞∫0 e-0,1x cosx dx |
0∫-∞ [x√(1+x2)] -1dx |
∞∫-∞ x(x+1) -3 dx |
1∫0 {e 1/x / x3 }dx |
30 |
|