Evalute : 1 x^2-8 x-20 d x - Vidyadip

Question

Evalute : $\int \frac{1}{\sqrt{x^2-8 x-20}} d x$

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Answer

$
\begin{aligned}
& \int \frac{1}{\sqrt{x^2-8 x-20}} d x \\
= & \int \frac{1}{\sqrt{\left(x^2-8 x+16\right)-16-20}} d x \\
= & \int \frac{1}{\sqrt{(x-4)^2-(6)^2}} d x \\
= & \log \left|(x-4)+\sqrt{(x-4)^2-(6)^2}\right|+c \\
= & \log \left|(x-4)+\sqrt{x^2-8 x-20}\right|+c .
\end{aligned}
$

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