Show that `int_(0)^(pi//2) (x)/(sinx+cosx)dx=(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)

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

int_(0)^(pi//2)(cosx)/((sinx+cosx))dx=(pi)/(4)

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

int_(0)^(pi//2)(sinx)/(sqrt(1+cosx))dx

show that int_(0)^(pi//2)(sinx-cosx)log(sinx+cosx)dx=0

int_(0)^(pi//2)(sqrt(sinx)cosx)^(3)dx=?