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1=int(0)^( pi)x log(sin x)dx-C...

1=int_(0)^( pi)x log(sin x)dx-C

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

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

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

int_(0)^( pi)cos2x*log(sin x)dx

If I_(1)=int_(0)^(pi//2)log (sin x)dx and I_(2)=int_(0)^(pi//2)log (sin 2x)dx , then

int_ (0) ^ (pi) x log sin xdx

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

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

Show that int_(0)^(pi//2) log (sin x) dx = - pi/2 log 2