`int_0^((pi)/(4)) log (1 + 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

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

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

int_ (0) ^ ((pi) / (4)) log (1 + tan theta) dth eta

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

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

int_(0)^(pi//2) log (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)

int_ (0) ^ ((pi) / (4)) ln (1 + tan theta) d theta

The value of the definite integral int_(0)^((pi)/(3))ln(1+sqrt(3)tan x)dx equals -