If d x x 1-x^3 = k ( 1-x^3 -1 1-x^3 +1 )+ c ,( where c is a constant of integration), then value of k is

Step-by-step solution

aligned & Let I = d x x 1-x^3 & = x^2 ~d x x^3 1-x^3 ~d x & Put 1-x^3= t ^2 & -3 x^2 ~d x=2 tdt & x^2 ~d x= -2 tdt 3 & aligned aligned I & = - ( 2 tdt 3 ) (1- t ^2 ) t & =- 2 3 1 1- t ^2 dt & = 2 3 1 t ^2-1 dt & = 2 3 1 2 | t -1 t +1 |+ c & = 1 3 | 1-x^3 -1 1-x^3 +1 |+ c k & = 1 3 aligned