`int_(0)^((pi)/(2))(dx)/(2cosx+4sinx)=(1)/(sqrt(5))log((3+sqrt(5))/(2))`

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

int_(0)^((pi)/(2))(dx)/(4+5cosx)=(1)/(3)log2

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) .

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

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

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

int_(0)^(pi)(cosx)/(sqrt(4+3sinx))dx is