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Question

Solve:
$\int \frac{2}{(1 - x) (1 + x)}$

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Solution

$\int \frac{2}{(1 - x) (1 - x)} d x$
$= \int \frac{(1 - x) + (1 + x)}{(1 - x) (1 + x)} d x$
$= \int \frac{1}{1 + x} d x + \int \frac{1}{1 - x} d x$
$= l o g (1 + x) - l o g (1 - x) + c$
$= l o g ∣ ∣ ∣ \frac{1 + x}{1 - x} ∣ ∣ ∣ + c$
$∴ \int \frac{2}{(1 - x) (1 + x)} d x = l o g ∣ ∣ ∣ \frac{1 + x}{1 - x} ∣ ∣ ∣ + c$

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