Evalute : 1 x^2+4 x+29 d x - Vidyadip

Question

Evalute : $\int \frac{1}{\sqrt{x^2+4 x+29}} d x$

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Answer

$
\begin{aligned}
& \int \frac{1}{\sqrt{x^2+4 x+29}} d x \\
= & \int \frac{1}{\sqrt{\left(x^2+4 x+4\right)+25}} d x \\
= & \int \frac{1}{\sqrt{(x+2)^2+(5)^2}} d x \\
= & \log \left|(x+2)+\sqrt{(x+2)^2+(5)^2}\right|+c
\end{aligned}
$
$
=\log \left|(x+2)+\sqrt{x^2+4 x+29}\right|+c \text {. }
$

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