14x2dx 122x2dx 12arctg x2 C
1x2-4dx 1x2-22dx 14 lnx-2x2 C
14-x2dx 122-x2dx arcsin x2 C
1x24dx lnxx24 C
1x2-4dx lnx x2-4 C
(3x5)4dx (3x5)4d(3x5)
13 (3x5)4d(3x5) 13 (3x5)4141 C
(3x5)515 C
sin4x cosxdx sin4xd( sinx) sin5x5 C
(x23)5xdx 12 (x23)5d(x23)
12 (x23)5151 C (x23)612 C
x2ex3dx 13 ex3d(x3) 13 ex3 C
dx3x5 13 d(3x5)3x5 13 ln3x5 C
ex5ex7dx 15 d(5ex 7)5ex7 15 ln5ex7 C
(5sinx14-30x116x - 8x29) dx
5sinxdx 14dx-30 x11dx 61x dx - 8dxx29 -5cosx 14x - 30x1212 6 lnx - 8arctg x3 C
x23x4 dx (x2)x-43dx xx-43dx 2x-43dx
x-13dx 2x-43dx x-131-131 2x-13-13 C
3x2323 - 2x-13 3 C 323x2 - 63x C.
x25x24dx x241x24dx x24x24dx 1x24dx
dx 1x222dx x 12 arctg x2 C
x4x21dx (x4-1)1x21 dx x2-1x211x21 dx
(x2-1)dx 1x21 dx x2dx - dx 1x212dx x33 - x arctg x C
x42x2(x-1)dx x42x3-x2dx (x1)dx x22x3-x2dx
x42 x3-x2
x4-x3 x1
-x32
x3-x2
x2 2
xdx dx x22x3-x2 dx
01x3x81dx 14 01d(x4)(x4 21 14 arctg x4
14 ( arctg1 - arctg 0 ) 14 (PI4 - 0) PI16
66
26x-2dx 26(x-2)12d(x-2) (x-2)3232 23 ((x-2)3
22
23 ( (6-2)3- (2-2)3) 23 ( 223 - 0 )
23 ( 8-0) 163
34x23х-2 dx x23 x-2
x2-2x
x 2
-2x3
-2x- 4
-7
34xdx 342xdx 347x-2 dx
4
( x22 2x 7 lnx-2)
3
(422 24 7 ln4-2)-(322 23
7ln( 3-2) 887ln2-4,5-6-7ln1
5,5 7ln2 .
Непосредственное интегрирование.
Вычислить интеграл :23х3-x2x2х dx 23x2( x2-1)х( х1 )dx 23х х-1 ( х1 )х1dx 23хх-1dx
23(x2-х)dx 23x2dx - 23xdx x33 - x22 333 - 233 - 322 222 236
Метод подстановки
2x3 1 u3
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