不定积分的典型例题

例35．

x3(1 x)

2

2

3

2

x tant

1 x2

x2 c.

例36． 例37

x ax4

2

dx

x asecta 0

1 x2 a2

2 x3a

c.

3

dx1 x2

x sint

costcost cos2t dt 2

1 cost1 cost1 x2

arcsinx c.

xx

例38．

()7 2 t

11

ln2 x7 lnx c.142

例39．

dxdx

33 123222

(1 x x)[(x ) ]

24

11

x 2t

dx

x(x7 2)

x

1t

t

(

1)dtt2

tdt2(2x 1)

c.3

3223 x x2(1 t)

4

例40．

x2exx2ex1x 2x2x

dx (xe)dx e c. (x 2)2 x 2x 2x 2例41．

dxx9dx1110

lnx ln(x 2) c. x(2 x10) x10(2 x10)220*例42．

(1 x7)dx(1 x7)x6dx2 lnx ln1 x7 c. x(1 x7) x7(2 x10)7例43．