BITSAT2023MathematicsIndefinite IntegrationActual
⁻¹ x dx is equal to
Options
- A(x+1) ⁻¹ x - x +C
- Bx ⁻¹ x - x +C
- Cx -x ⁻¹ x +C
- Dx -(x+1) ⁻¹ x +C
Correct answer
A. (x+1) ⁻¹ x - x +C
Step-by-step solution
We have, I= 1 ⁻¹ x dx Using by parts, aligned I & = ⁻¹ x (x)- 1 1+x 1 2 x x d x & =x ⁻¹ x - x (1+x) 2 x d x & =x ⁻¹ x - ( 1+x (1+x) 2 x - 1 (1+x) 2 x ) d x & =x ⁻¹ x - d x 2 x + d x 2 x (1+x) & =x ⁻¹ x - x + ⁻¹ x +C & =(x+1) ⁻¹ x - x +C aligned