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

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

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

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

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

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

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

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

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

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