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

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 $9$

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

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Answer

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