Indefinite Integration
Integration by Substitution
JEE Main 2020
Grade 12
Question:
$\int x e^{x^2} \, dx$ equals:
(1) $\frac{1}{2} e^{x^2} + C$
(2) $e^{x^2} + C$
(3) $2 e^{x^2} + C$
(4) $\frac{1}{2} x^2 e^{x^2} + C$
Step-by-Step Solution
Key Concept: Substitute $t = x^2$ so that $dt = 2x \, dx$, reducing the integral to the elementary exponential form $\int e^t \, dt$ (up to a constant factor).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)