Indefinite Integration
Standard Integrals
IIT-JEE 2010
Grade 12
Question:
$\int \left(1 + x - \frac{1}{x}\right) e^{x + \frac{1}{x}} \, dx$ equals:
(1) $x e^{x + \frac{1}{x}} + C$
(2) $e^{x + \frac{1}{x}} + C$
(3) $x^2 e^{x + \frac{1}{x}} + C$
(4) $\frac{1}{x} e^{x + \frac{1}{x}} + C$
Step-by-Step Solution
Key Concept: Try the guess $F(x) = x e^{x + 1/x}$ and differentiate it using the product rule — compare the result with the given integrand.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)