Indefinite Integration
Integration by Parts
Premium Question
Grade 12
Question:
$\int \frac{x e^x}{(x + 1)^2} \, dx$ equals:
(1) $\frac{e^x}{x + 1} + C$
(2) $-\frac{e^x}{x + 1} + C$
(3) $\frac{e^x}{(x + 1)^2} + C$
(4) $x e^x + C$
Step-by-Step Solution
Key Concept: Write $\frac{x}{(x + 1)^2} = \frac{1}{x + 1} - \frac{1}{(x + 1)^2}$ and recognise the resulting expression as the derivative (via the quotient rule) of $\frac{e^x}{x + 1}$.
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Correct Answer: (1)