integral from 0 to pi of xsin(x)/(1+cos^2(x)) dx : Calculus

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integrate 0 to pi integrate 0 to pi '(xsinx)/(1+cos^2x) dx || Evaluate `int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx`.
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Evaluate `int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx`. Evaluate `int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx`.
Definite integrals ; Integral 0 to pi x sin x by 1+cosĀ²x @EAG Definite integrals ; Integral 0 to pi x sin x by 1+cosĀ²x @EAG
`int_(0)^((pi)/(2))(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)` `int_(0)^((pi)/(2))(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)`
Show that 0 to pi/2 integral x/sinx+cosx dx = Ļ€/2āˆš2 log (āˆš2+1) || Vvvip || Definite Integration Show that 0 to pi/2 integral x/sinx+cosx dx = Ļ€/2āˆš2 log (āˆš2+1) || Vvvip || Definite Integration
Integral 0 to pi x SinĀ³x / 1+CosĀ²x dx , #definiteintegrals @EAG Integral 0 to pi x SinĀ³x / 1+CosĀ²x dx , #definiteintegrals @EAG