§1 不定积分

3）d???u?1?2??u?1???arcsin2???1?2C?1?21?2?????u?2??2?arcsin?2u?1??C?arcsin?2lnx?1??C.

?x31?x2dx；

29

（

解 原式??x31?xdx

u?x2212122??x1?xdx??????u1?udu 221???u?1?1?1?udu23111???u?1?2d?u?1????u?1?2d?u?1?22 30

1?22????u?1???u?1???C2?53?

523212?1?x5??5212?1?x3??32?C.（4）?esin2x?sinx； dx2xesin2x?2x2解 原式??e

?sinxdx

231

1sin2x?2x???ed?sin2x?2x?

41sin2x?2x??e?C.

41?x（5）?； dxxx1?xe???x?xxx?xe?e?xe?1?xe ???????? 32