d x x^ 2 +2 x+2 equals - Vidyadip

Question

$\int \frac{d x}{x^{2}+2 x+2}$ equals

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Answer

$\int \frac{d x}{x^{2}+2 x+2}=\int \frac{d x}{\left(x^{2}+2 x+1\right)+1}$
$= \int \frac{1}{(x+1)^{2}+(1)^{2}} d x$
$=\left[\tan ^{-1}(x+1)\right]+C$

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