求∫tanx/(1-(tanx)^2)dx

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求∫tanx/(1-(tanx)^2)dx
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求∫tanx/(1-(tanx)^2)dx
求∫tanx/(1-(tanx)^2)dx

求∫tanx/(1-(tanx)^2)dx

=∫cosxsinx/[cos^2 x-sin^2 x] dx
=∫sinx/[cos^2 x-sin^2 x] d(sinx)
=∫1/2*1/[cos^2 x-sin^2 x] d(sin^2 x)
=∫1/2*1/[1-2sin^2 x] d(sin^2 x)
=-1/4∫ 1/[sin^2 x-1/2] d(sin^2 x-1/2)
=-1/4 ln |sin^2 x-1/2|