`int_(0)^((pi)/(2))log(tanx)dx=0`

Prove that int_(0)^((pi)/(4))log(1+tanx)dx=(pi)/(8)log2

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(4))log(1+tanx)dx

Evaluate : int_(0)^(pi/2)log(tanx)dx

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

int_(0)^(pi//4)log(1+tanx)dx=

int_(0)^((pi)/(2)) log (cotx)dx is :

Prove that int_(0)^((pi)/(2)) log ( tan x ) dx = 0

int_(0)^(pi//2)log(tanx+cotx)dx=