计算不定积分∫（xsinx）/（cos³x）dx等 - 知识问答

计算不定积分∫（xsinx）/（cos³x）dx等于多少?

1个回答

∫ xsinx/cos³x dx
= ∫ xsec²xtanx dx
= ∫ xsecx dsecx
= (1/2)∫ x dsec²x
= (1/2)xsec²x - (1/2)∫ sec²x dx
= (1/2)xsec²x - (1/2)tanx + C
= (1/2)(xsec²x - tanx) + C

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