int_(0)^(4)(pi x-4x^(2))ln(1+tan x)dx=

int_(0)^( pi/4)(pi x-4x^(2))ln(1+tan x)backslash dx=

The value of int_( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

The value of int_( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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

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

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

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