∫1x^2 4dx= 14∫(x+2) (x 2)(x 2)(x+2)dx= 14∫1x 2dx 14∫1x+2dx= 14ln(x 2) 14ln(x+2)+c #160; #160; #160; #160; #160; #160; # ...

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Chain Rule of Differentiation

Solve ∫ 1x...

Question

Solve
$\int$ $\frac{1}{x^{2} - 4} d x$

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Solution

$\int \frac{1}{x^{2} - 4} d x =$

$\frac{1}{4} \int \frac{(x + 2) - (x - 2)}{(x - 2) (x + 2)} d x =$

$\frac{1}{4} \int \frac{1}{x - 2} d x - \frac{1}{4} \int \frac{1}{x + 2} d x =$

$\frac{1}{4} ln (x - 2) - \frac{1}{4} ln (x + 2) + c$

$= \frac{1}{4} ln (\frac{x - 2}{x + 2}) + c$

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