# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

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

Learn how to solve integrals of rational functions problems step by step online. Integral of 1/(x^2-x-2) with respect to x. Factor the trinomial x^2-x-2 finding two numbers that multiply to form -2 and added form -1. Thus. Rewrite the fraction \frac{1}{\left(x+1\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by \left(x+1\right)\left(x-2\right).

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 1.56 seconds