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

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

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

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

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

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3. int_(0)^( pi/2)( sin2 x)/(1+cos^(2)x)dx

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