Evalute : d x 3-2 x-x^2 d x - Vidyadip

Question

Evalute : $\int \frac{d x}{3-2 x-x^2} d x$

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Answer

$
\begin{aligned}
& \int \frac{d x}{3-2 x-x^2}=\int \frac{d x}{3-\left(x^2+2 x+1\right)+1} \\
= & \int \frac{1}{(2)^2-(x+1)^2} d x \\
= & \frac{1}{2 \times 2} \log \left|\frac{2+x+1}{2-x-1}\right|+c \\
= & \frac{1}{4} \log \left|\frac{3+x}{1-x}\right|+c .
\end{aligned}
$

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