不定积分的典型例题

1 t21

222

dx 1 t22t1 t2 (1 t2)(1 t)1

1 t21 t2 1t 1

( )dt

t 1t2 1

1

lnt 1 ln(t2 1) arctant c

2

1x ln(1 sinx) c.

22

*例6 x2x2 1dx 1422 x xdx2

112121112222

(x ) ()d(x ) u ()du 222222

分部积分

1111

uu2 ()2 ln(u u2 ()2) c4216211

x(2x2 1)x2 1 lnx x2 1 c.88

(x 1)2

22

x (x 2x x2)dx分项

3

1

1

例7

45

2x x x c.

32

3

252

例8．

1111 [ 1 x42 1 x21 x2]dx

11 x1 ln arctanx c. 41 x2

例9．

x1 x 1 dx x x

124

dx x x x c.

33 x

xdx

例10．