If d x (1+ x ) x-x^2 = A x 1-x + B 1-x +C , where C is real constant, then A+B equals to

Step-by-step solution

Given, d x (1+ x ) ( x^2-x^2 ) = A x 1-x + B 1-x +c On differentiating both sides, we get aligned & 1 (1+ x ) ( x-x^2 ) & = 1-x (A 1 2 x )-(A x +B) 1 2 2-x (-1) ( 1-x )^2 & 1 (1+ x ) ( x-x^2 ) = (1-x) A+A x+B x (1-x) 2 x (1-x) & 2(1-x) (1+ x ) =A+B x & 2-2 x =A+B x & A=2, B=2 & A-B=0 & aligned