# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

$\begin{matrix}u=x+5 \\ du=dx\end{matrix}$

Learn how to solve integrals of rational functions problems step by step online. Integral of 1/((x+5)^2+4) with respect to x. Solve the integral \int\frac{1}{\left(x+5\right)^2+4}dx applying u-substitution. Let u and du be. Substituting u and dx in the integral and simplify. Factor the integral's denominator by 4. Resolver la integral aplicando la sustitución v^2=\frac{1}{4}u^2.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.95 seconds