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int0^pi (2x(1+ sin x))/(1+cos^2 x) dx...

`int_0^pi (2x(1+ sin x))/(1+cos^2 x) dx`

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Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

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If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to

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int_(0)^(pi//2) (sin x)/(1 +cos^2) dx .

int_(0)^( pi/2)(sin x)/(1+cos x)dx

int_(0)^( pi)(sin x)/(1+cos^(2)x)dx =