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Step-by-step Solution

Integral of $\frac{2x+8}{x^2+9x+20}$ with respect to x

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\frac{2x+8}{x^2+9x+20}dx$
1

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

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

$\int\frac{2x+8}{\left(x+4\right)\left(x+5\right)}dx$

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Answer

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

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