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int(0)^( pi)((2x+3)sin x)/((1+cos^(2)x))...

int_(0)^( pi)((2x+3)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)

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

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

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

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

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

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

If int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to: