d d x [a ⁻¹ x+b ( x-1 x+1 ) ]= 1 x^4-1 a-2 b is equal to

Step-by-step solution

Given, d d x [a ⁻¹ x+b ( x-1 x+1 ) ]= 1 x^4-1 On integrating both sides, we get aligned & a ⁻¹ x+b ( x-1 x+1 ) & = 1 2 [ 1 x^2-1 - 1 x^2+1 ] d x & a ⁻¹ x+b ( x-1 x+1 ) & = 1 4 ( x-1 x+1 )- 1 2 ⁻¹ x & a=- 1 2 , b= 1 4 & a-2 b=- 1 2 -2 ( 1 4 )=-1 aligned