xcoslnx xsinlnx coslnxdx, x
所以 coslnxdx (coslnx sinlnx) C.
2
21. (arcsinx)2dx;
解 (arcsinx)2dx x(arcsinx)2 x 2arcsinx x(arcsinx)2 2 arcsinxd x2 x(arcsinx)2 2 x2arcsinx 2 dx
1 x
2
dx
22. exsin2xdx. 解 exsin2xdx
excos2x 2 sin2xdex excos2x 2exsin2x 4 excos2xdx, 1
excos2xdx ex(cos2x 2sin2x) C,
5
11
所以 exsin2xdx ex ex(cos2x 2sin2x) C.
210
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而 excos2xdx cos2xdex excos2x 2 exsin2xdx
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(1cos2)e xdx e ecos2xdx, 2 22
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x(arcsinx)2 2 x2arcsinx 2x C.