# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve integrals of polynomial functions problems step by step online. Integral of 2x+(x+5)/(x^2-2x-8). The integral of the sum of two or more functions is equal to the sum of their integrals. The integral \int2xdx results in: x^2. The integral \int\frac{x+5}{x^2-2x-8}dx results in: -\frac{1}{2}\ln\left|x+2\right|. The integral \int\frac{\frac{3}{2}}{x-4}dx results in: \frac{3}{2}\ln\left|x-4\right|.

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

### Problem Analysis

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

### Main topic:

Integrals of polynomial functions

~ 0.12 seconds