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

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

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

Prove that int_(0)^((pi)/(2))(sin^(2)x)/(1+sin x cos x)dx=(pi)/(3sqrt(3))

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

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

int_(0)^((pi)/(4))sqrt(1+sin2x)dx

int_(0)^((pi)/(4)) sqrt(1+sin 2x) dx =

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

int_(0)^(pi//4)sqrt((1-sin2x)/(1+sin 2x))dx=

int_(0)^( pi//2)sqrt((1-sin2x)/(1+sin2x))dx