Indefinite Integration
Rational Functions
Premium Question
Grade 12
Question:
$\int \frac{x}{(x + 1)^2} \, dx$ equals:
(1) $\ln |x + 1| + \frac{1}{x + 1} + C$
(2) $\ln |x + 1| - \frac{1}{x + 1} + C$
(3) $-\ln |x + 1| + \frac{1}{x + 1} + C$
(4) $\ln |x + 1| + \frac{1}{(x + 1)^2} + C$
Step-by-Step Solution
Key Concept: Write $\frac{x}{(x + 1)^2} = \frac{(x + 1) - 1}{(x + 1)^2}$ and split it into two simpler fractions before integrating term by term.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)