∫(1+tan^2x)dx/(1+tanx)^3

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∫(1+tan^2x)dx/(1+tanx)^3
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∫(1+tan^2x)dx/(1+tanx)^3
∫(1+tan^2x)dx/(1+tanx)^3

∫(1+tan^2x)dx/(1+tanx)^3
见图

∫(1+tan^2x)dx/(1+tanx)^3
=∫sec^2xdx/(1+tanx)^3
=∫1/(1+tanx)^3d(1+tanx)
=-2*1/(1+tanx)^2+C

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