高等数学A上册习题解答 至微分中值定理(18)

华中师范大学专用

(4)

(arcsinx)2dx

1

=x(arcsinx)2 x2arcsinxdx=x(arcsinx)2+ 2arcsinxd

1 x2

=x(arcsinx)2

+2 1 x2arcsinx 1 x22dx

=x(arcsinx)2

+2 1 x2arcsinx 2x+C.(5)

exsin2xdx=1 ex(1 cos2x)dx=1x1

2e 2

excos2xdxÏ §

excos2xdx=

cos2xdex

=ex

cos2x+2 exsin2xdx

=ex

cos2x+2

sin2xde

x

=excos2x+2[exsin2x

2excos2xdx]=excos2x+2exsin2x 4

excos2xdx]

¤±

excos2xdx

=1

5

[excos2x+2exsin2x]+C18

(0.47)

(0.48)

(0.49)

(0.50)