求∫exsin2xdx.

admin2016-09-13  28

问题 求∫exsin2xdx.

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答案∫exsin2xdx=∫ex[*](1-cos2x)dx=[*]∫excos2xdx, 而 ∫excos2xdx=∫cos2xdex=excos2x+2∫sin2x.exdx =excos2x+2∫sin2xdex=excos2x+2exsin2x-4∫excos2xdx, 所以 ∫excos2xdx=[*]excos2x+[*]exsin2x+C1, 于是 ∫exsin2xdx=[*]ex-[*]excos2x-[*]exsin2x+C(C=[*]C1).

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