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

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

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

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

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

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)