Question
Evalute : $\int \frac{2 x+6}{\sqrt{x^2+6 x+3}} d x$

Answer

$
\text { Let } I=\int \frac{2 x+6}{\sqrt{x^2+6 x+3}} d x
$
Put $x^2+6 x+3=t$
$
\begin{aligned}
& \therefore(2 x+6) d x=d t \\
& \therefore I=\int \frac{1}{\sqrt{t}} d t=\int t^{-\frac{1}{2}} d t
\end{aligned}
$
$
=\frac{t^{\frac{1}{2}}}{1 / 2}+c=2 \sqrt{x^2+6 x+3}+c .
$

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