8.int_(0)^((pi)/(4))log(1+tan x)dxquad 9.int_(0)^(2)x

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

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

int_(0)^((pi)/(2))sin2x*log(tan x)dx=

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

int_(0)^((pi)/(2))(1)/(cot x+tan x)dx

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)

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