Integrals
NCERT Class 12
CBSE
Grade 12
Question:
$\int \dfrac{x e^x}{(1 + x)^2} dx$ is equal to:
(a) $\dfrac{e^x}{1 + x} + C$
(b) $\dfrac{-e^x}{1 + x} + C$
(c) $\dfrac{e^x}{(1 + x)^2} + C$
(d) $\dfrac{x e^x}{1 + x} + C$
Step-by-Step Solution
$\int e^x \left[ \dfrac{1}{1+x} - \dfrac{1}{(1+x)^2} \right] dx = \dfrac{e^x}{1+x} + C$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Evaluating integral $= e^x/(1+x) + C$: 1.0 Mark
Correct Answer: $\dfrac{e^x}{1 + x} + C$
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.