`int_0^(pi/2) cos^2x/(sinx+cosx)dx=1/sqrt2(log(sqrt2+1))`

int_0^(pi/2) (cos x)/(sinx + cosx) dx =

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

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

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

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)