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Prove that int(0)^(pi//2)log (sinx)dx=in...

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

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

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 (cotx ) dx=

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

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

int_(0)^(pi) x log sinx\ dx