Show that : `int_0^(pi/2)(sin^2x)/(sinx+cosx)dx=1/(sqrt(2))log(sqrt(2)+1)`

Show that int_(0)^(pi//2) (x)/(sinx+cosx)dx=(pi)/(2sqrt(2))log (sqrt(2)+1) .

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

Using properties of definite integrals, show that int_(0)^(pi//2)(xdx)/(sinx+cosx)=(pi)/(2sqrt(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)|

int_(0)^((pi)/(2))(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)

int_0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =