Evalute : 1 3 x^2+8 d x - Vidyadip

Question

Evalute : $\int \frac{1}{\sqrt{3 x^2+8}} d x$

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Answer

$
\begin{aligned}
& \int \frac{1}{\sqrt{3 x^2+8}} d x=\int \frac{1}{\sqrt{(\sqrt{3} x)^2+(\sqrt{8})^2}} d x \\
= & \frac{\log \left|\sqrt{3} x+\sqrt{(\sqrt{3} x)^2+(\sqrt{8})^2}\right|}{\sqrt{3}}+c \\
= & \frac{1}{\sqrt{3}} \log \left|\sqrt{3} x+\sqrt{3 x^2+8}\right|+c .
\end{aligned}
$

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