§1 不定积分

解 原式??x1?xeex??1?x?exx? dxxx??dxexex??????du ?u?1?u??1?xe?u?xex1?11?1????du?du?du???u1?u ?u1?u??lnu?ln1?u?C

33

uxe ?ln?C?ln?C.x1?u1?xeln?tanx?dx. （6）?sinx?cosxx??1?secx lntanx????????tanxsinx?cosx???lntanx解 原式??ln?tanx?d? ????

34

212例解

?2ln?tanx??C. 求 ?ln?x?1?x2?1?x2dx.

原式??ln?x?1?x2?d??2??ln?x?1?x????2?23??ln?x?1?x?3?2???C. 35

2

e?e例3 求 ?4x. dx2x3xx解例

e?2e?12xx?原式??e?e?ex?e2x??ex?e?x?2dx x?x??de?e??ex?e?x?2??1ex?e?x?C. 24 求 ?x?1x4?1dx.

36