Final answer to the problem
$\frac{1}{2}\ln\left|x-3\right|+\frac{1}{2}\ln\left|x+3\right|-\frac{1}{6}\ln\left|x-3\right|+\frac{1}{6}\ln\left|x+3\right|+C_0$
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Step-by-step Solution
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1
Expand the fraction $\frac{x-1}{x^2-9}$ into $2$ simpler fractions with common denominator $x^2-9$
$\int\left(\frac{x}{x^2-9}+\frac{-1}{x^2-9}\right)dx$
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$\int\left(\frac{x}{x^2-9}+\frac{-1}{x^2-9}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x-1)/(x^2-9))dx. Expand the fraction \frac{x-1}{x^2-9} into 2 simpler fractions with common denominator x^2-9. Expand the integral \int\left(\frac{x}{x^2-9}+\frac{-1}{x^2-9}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x}{x^2-9}dx results in: \frac{1}{2}\ln\left(x+3\right)+\frac{1}{2}\ln\left(x-3\right). Gather the results of all integrals.
Final answer to the problem
$\frac{1}{2}\ln\left|x-3\right|+\frac{1}{2}\ln\left|x+3\right|-\frac{1}{6}\ln\left|x-3\right|+\frac{1}{6}\ln\left|x+3\right|+C_0$
