AP EAMCET2007MathematicsIndefinite Integration
⁻¹ ( 1-x 1+x ) d x is equal to
Options
- A1 2 (x ⁻¹ x- 1-x^2 )+c
- B1 2 (x ⁻¹ x+ 1-x^2 )+c
- C1 2 (x ⁻¹ x- 1-x^2 )+c
- D1 2 (x ⁻¹ x+ 1-x^2 )+c
Correct answer
A. 1 2 (x ⁻¹ x- 1-x^2 )+c
Step-by-step solution
Let I= ⁻¹ 1-x 1+x d x Put x= 2 aligned I & = ⁻¹ 1- 2 1+ 2 d x & = ⁻¹ ^2 d x & = d x & = 1 2 1 ⁻¹ x d x & = 1 2 [ ⁻¹ x x+ x 1-x^2 d x ] & = 1 2 [x ⁻¹ x- 1-x^2 ]+c aligned