高等数学A上册习题解答 至微分中值定理(19)

华中师范大学专用

(5)

exsin2xdx

=12ex 1

2

excos2xdx=1

11ex excos2x exsin2x+C2. f(x)=sinx

,¦xf (x)dx):

xf (x)dx=

xdf (x)

=xf (x)

f (x)dx=xf (x) f(x)+C

=cosx 2sinx

x

+C.3. f(x)=xex§¦

f (x)lnxdx. f (x)lnxdx

=

lnxdf(x)

=f(x)lnx

f(x)

xdx=f(x)lnx

exdx=xexlnx ex+C.

19

(0.51)

(0.52)

(0.53)