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

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

Evaluate (i) int_(0)^(pi//2)(d x)/(1+sqrt(tan x)) (ii) int_(0)^(pi//2) log (tan x ) d x (iii) int_(0)^(pi//4) log (1+tan x ) d x (iv) int_(0)^(pi//2)(sin x- cos x)/(1+ sin x cos x)d x

The value of the integral int _(0)^(pi//2) log | tan x| dx is

If int_(0)^(pi//2) log(cosx) dx=pi/2 log (1/2), then int_(0) ^(pi//2) log (sec x ) dx =

int_(0)^(pi//2) sin 2x log (tan x) dx is equal to

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

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

int_(0)^(pi//2) sin 2x log tan x dx is equal to