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Step-by-step Solution

Integral of $\frac{1}{x^2-x-2}$ with respect to x

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Answer

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

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 $-1$

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

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

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Answer

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