Indefinite Integration
Forms Involving e^x
Premium Question
Grade 12
Question:
$\int e^x \left(\frac{x - 2}{x^3}\right) \, dx$ equals:
(1) $-\frac{e^x}{x^2} + C$
(2) $\frac{e^x}{x^2} + C$
(3) $-\frac{e^x}{x} + C$
(4) $\frac{e^x}{x} + C$
Step-by-Step Solution
Key Concept: Split the integrand as $e^x \left(\frac{1}{x^2} - \frac{2}{x^3}\right)$ and recognise it in the form $e^x [f(x) + f'(x)]$ for a suitable $f(x)$.
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Correct Answer: (1)