# Integral of (2x+8)/(9x+20+x^2)

## Answer

$2\ln\left|5+x\right|+C_0$

## Step-by-step explanation

Problem

$\int\frac{2x+8}{x^2+9x+20}dx$

1

Factor the trinomial $20+9x+x^2$ finding two numbers that multiply to form $20$ and added form $9$

$\begin{matrix}\left(4\right)\left(5\right)=20\\ \left(4\right)+\left(5\right)=9\end{matrix}$

## Answer

$2\ln\left|5+x\right|+C_0$