VITEEE2013MathematicsDefinite Integration
(1+x-x⁻¹ ) e^ x+x⁻¹ d x is equal to
Options
- A(x+1) e ^ x+x⁻¹ +C
- B(x-1) e ^ x+x⁻¹ +C
- Cx e^ x+x⁻¹ +C
- Dx e^ x+x⁻¹ x+C
Correct answer
C. x e^ x+x⁻¹ +C
Step-by-step solution
(1+x-x⁻¹ ) e^ x+x⁻¹ d x= [x e^ x+x⁻¹ (1- 1 x² )+e^ x+x⁻¹ ] d x [ x f^ (x)+f(x) d x=x f(x)+C ] (1+x-x⁻¹ ) e^ x+x⁻¹ d x=x e^ x+x⁻¹ +C