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Step-by-step Solution

Integral of $2x+\frac{x+5}{x^2-2x-8}$

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Answer

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

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

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

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Answer

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