int_(0)^( pi/2)ln(tan x)dx

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

int_0^(pi//2) log(tan x)dx =

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

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

int_0^(pi//2) log(tan x) dx is :

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

Prove that: int_(0)^( pi/2)log|tan x+cot x|dx=pi log_(e)2

Which of the following are false : Statement-I : ( int_(0)^(pi//2) (sqrt(cos x))/(sqrt(cos x + sqrt(sin x)))= pi/2 Statement-II : int_(0)^(pi//2) log(tan x) dx=1 Statement-III: int_(0)^(pi//2) log sin x dx = - pi log 2

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=