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Step-by-step Solution

Integral of $\frac{1}{\left(x+5\right)^2+4}$ with respect to x

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Answer

$\frac{1}{2}arctan\left(\frac{1}{2}\left(x+5\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{dx}{\left(x+5\right)^2+4}$
1

Solve the integral $\int\frac{1}{\left(x+5\right)^2+4}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x+5 \\ du=dx\end{matrix}$
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Substituting $u$ and $dx$ in the integral and simplify

$\int\frac{1}{u^2+4}du$

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Answer

$\frac{1}{2}arctan\left(\frac{1}{2}\left(x+5\right)\right)+C_0$