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" 4.सिद्ध कीजिए कि "int(0)^( pi/2)log(ta...

" 4.सिद्ध कीजिए कि "int_(0)^( pi/2)log(tan x)dx=0" ."

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int_(0)^(pi//2)log(tanx)dx=

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

int_(0)^(pi//2)log(sinx)dx=

int_(0)^(pi//2)log(cosx)dx=

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

int_(0)^((pi)/(2))log(sin x)dx

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

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

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

int_(0)^((pi)/(2))log(sin2x)dx