计算∫arctanexdx.

admin2021-10-18  31

问题 计算∫arctanexdx.

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答案∫arctanex/exdx=∫arctanex/e2xd(ex)=∫arctant/t2dt=-∫arctantd(1/t)=-arctant/t+∫1/[t(1+t2)]dt=-arctant/t+∫(1/t-t/(1+t2))dt=-arctant/t+lnt-1/2lm(1+t2)+C=arctantex/ex+1/2lne2x/(1+ex)+C.

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