If d d x (A ( 1-x^3 +B 1-x^3 +1 ) )= 1 x 1-x^3 , then A B=

Step-by-step solution

We have d dx ( A ( 1- x ^3 + B 1- x ^3 +1 ) )= 1 x 1- x ^3 now integrating both sides aligned & 1 x 1-x^3 d x=A ( 1-x^3 +B 1-2^3 +1 )+c & = 3 x^2 d x x^3 1-x^3 & put 1-x^3 =t x^3=1-t^2 & 1 2 (1-x^3 )^ - 1 2 (-3 x^2 ) d x=d t & -3 2 x^2 d x 1-x^3 =d t & 1 3 2 t^2-1 d t & = 1 3 (t+1)-(t-1) (t+1)(t-1) d t & = 1 3 1 (t-1) - 1 (t+1) d t & = 1 3 [ 1-x^3 -1 1+x^3+1 ]+c & 1 3 , B=-1 aligned