Indefinite Integration
Integration by Substitution
IIT-JEE 1995
Grade 12
Question:
$\int e^x(1 + x) \sec^2(x e^x) \, dx$ equals:
(1) $\tan(x e^x) + C$
(2) $\sec(x e^x) + C$
(3) $x e^x \tan(x e^x) + C$
(4) $\tan(e^x) + C$
Step-by-Step Solution
Key Concept: Substitute $t = x e^x$ so that $dt = e^x(1 + x) \, dx$, turning the integral into a standard form involving $\sec^2 t$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)