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" 4."th Show that "int(0)^(n/2)(sin^(2)x...

" 4."th Show that "int_(0)^(n/2)(sin^(2)x)/(sin x+cos x)dx=(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)(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)|

Show that int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt(3))/(12)pi

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

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

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

int(1)/(sin x - cos x +sqrt(2))dx equals