AP EAMCET2003MathematicsIndefinite Integration
(1+x-x⁻¹ ) e^ x+x⁻¹ d x is equal to :
Options
- A(1+x) e^ x+x⁻¹ +C
- B(x-1) e^ x+x⁻¹ +C
- C-x e^ x+x⁻¹ +C
- Dx e^ x+x⁻¹ +C
Correct answer
D. x e^ x+x⁻¹ +C
Step-by-step solution
(1+x-x⁻¹ ) e^ x+x⁻¹ d x= e^ x+x⁻¹ d x+ (x- 1 x ) e^ x+x⁻¹ d x=e^ x+x⁻¹ d x- [ d d x (e^ x+x⁻¹ ) ] x d x+ (x- 1 x ) e^ x+x⁻¹ d x=x e^ x+x⁻¹ - (1- 1 x^2 ) x e^ x+x⁻¹ d x+ (x- 1 x ) e^ x+x⁻¹ d x=x e^ x+x⁻¹ - (x- 1 x ) e^ x+x⁻¹ d x+ (x- 1 x ) e^ x+x⁻¹ d x+C=x e^ x+x⁻¹ +C