" (ii) "int_(0)^( pi/2)(xdx)/(sin x+cos x)=(pi)/(2sqrt(2))log(sqrt(2)+1)" ."

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

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

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

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

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

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