If 2 ⁻¹ 1-x 1+x d x=A ⁻¹ x+B x 1-x^2 +C then A+B is equal to

Step-by-step solution

We have, 2 ⁻¹ 1-x 1+x d x=A ⁻¹ x+B x 1-x^2 +C Let I= 2 ⁻¹ 1-x 1+x d x Put x= 2 d x=-2 2 d I=- 2 ⁻¹ 1- 2 1+ 2 2 2 d =- 2 ⁻¹ 2 ^2 2 ^2 2 2 d =- 2 ⁻¹ ^2 2 2 d =- 2 ⁻¹ 2 2 d =- [ (2 )] 2 2 d =- 2 ^2 2 d =- (1- 4 ) d =- [ - 4 4 ]+C= [- 1 2 ⁻¹ x+ 1 4 2 2 2 ]+C= [- 1 2 ( 2 - ⁻¹ x )+ 1 2 1-x^2 x ]+C= 1 2 ⁻¹ x+ x 2 1-x^2 + (C- 4 ) But I=A ⁻¹ x+B x 1-x^2 +C A= 1 2 and B= 1 2 Hence, A+B= 1 2 + 1 2 =1