∫(π/2,0) 1/[1+(cosx)^2] dx的值

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∫(π/2,0)1/[1+(cosx)^2]dx的值∫(π/2,0)1/[1+(cosx)^2]dx的值∫(π/2,0)1/[1+(cosx)^2]dx的值(1/2)|[1/(sin^2x)(1+(c

∫(π/2,0) 1/[1+(cosx)^2] dx的值
∫(π/2,0) 1/[1+(cosx)^2] dx的值

∫(π/2,0) 1/[1+(cosx)^2] dx的值
(1/2)|[1/(sin^2x)(1+(cos^2x))]]d(cos^2x)
(1/2)|[1/(1-cos^2x)(1+(cos^2x)]d(cos^2x)
(1/4)|[1/(1-cos^2x)-1/(1+cos^2x]d(cos^2x)
-(1/4)|d[ln|1-cos^2x|]-(1/4)d[ln|1+cos^2x|]
=-(1/8)(ln|1-cos^2x|)^2-(1/8)(ln|1+cos^2x|)^2
=-(1/8)[(ln|1-cos^2x|)^2+(ln|1+cos^2x|)^2](π/2,0) =-无穷-(ln2)^2=-无穷