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Functions

Evaluate ∫d...

Question

Evaluate $\int \frac{d x}{x^{2} - 4 x + 13}$

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Solution

$\int \frac{d x}{x^{2} - 4 x + 13}$
$= \int \frac{d x}{{(x - 2)}^{2} - 4 + 13}$
$= \int \frac{d x}{{(x - 2)}^{2} + {(3)}^{2}}$
$= \frac{1}{3} {tan}^{- 1} (\frac{x - 2}{3}) + C$
Hence $\int \frac{d x}{x^{2} - 4 x + 13} = \frac{1}{3} {tan}^{- 1} (\frac{x - 2}{3}) + C$

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