Prove that ((2t−1)/(lnt−ln(1−t)))=∫^( 1) _( 0) t^x (1−t)^(1−x) dx and ∫^( 1) _( 0) ((2t−1)/(lnt−ln(1−t)))dt = (π/2)∫^( 1) _( 0) ((x(1−x))/(sin(πx)))dx