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Integration by Partial Fractions

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Question

Evaluate: $\int \frac{5 x - 2}{1 + 2 x + 3 x} d x$

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Solution

$\int \frac{5 x - 2}{1 + 2 x + 3 x} d x = \int \frac{(5 x + 1) - 3}{5 x + 1} d x = \int d x - 3 \int \frac{d x}{5 x + 1} = x - 3 ln ∣ 5 x + 1 ∣ + C$

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