# Step-by-step Solution

## Integral of 2x+(x+5)/(x^2-2x-8)

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### Videos

$x^2+\frac{3}{2}\ln\left|x-4\right|-\frac{1}{2}\ln\left|x+2\right|+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(2x+\frac{x+5}{x^2-2x-8}\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int2xdx+\int\frac{x+5}{x^2-2x-8}dx$
2

Take the constant out of the integral

$2\int xdx+\int\frac{x+5}{x^2-2x-8}dx$

$x^2+\frac{3}{2}\ln\left|x-4\right|-\frac{1}{2}\ln\left|x+2\right|+C_0$
$\int\left(2x+\frac{x+5}{x^2-2x-8}\right)dx$