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

int_(0)^((pi)/(2))log(tan x)*dx

The value of int_(0)^((pi)/(2))log(tan x)dx is equal to -

Using integral int_(0)^(-(pi)/(2))ln(sin x)dx=-int_(0)^( pi)ln(sec x)dx=-(pi)/(2)ln2 and int_(0)^((pi)/(2))ln(tan x)dx=0 and int_(0)^((pi)/(4))ln(1+tan x)dx=(pi)/(8)

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

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) .

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

Evaluate the integral int_(0)^(pi//4) log(1+tanx)dx

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