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Step-by-step Solution

Integral of 1/(x^2-x-2)

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Answer

$\frac{1}{3}\ln\left|x-2\right|-\frac{1}{3}\ln\left|x+1\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1}{x^2-x-2}dx$
1

Factor the trinomial $x^2-x-2$ finding two numbers that multiply to form $-2$ and added form $-1$

$\begin{matrix}\left(-2\right)\left(1\right)=-2\\ \left(-2\right)+\left(1\right)=-1\end{matrix}$
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Thus

$\int\frac{1}{\left(x-2\right)\left(x+1\right)}dx$

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Answer

$\frac{1}{3}\ln\left|x-2\right|-\frac{1}{3}\ln\left|x+1\right|+C_0$

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