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" 6.Show that "int(0)^((pi)/(2))(sin^(2)...

" 6.Show that "int_(0)^((pi)/(2))(sin^(2)x)/(sin x+cos x)=(1)/(sqrt(2))log(sqrt(2)+1)

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

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

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

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