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Step-by-step Solution

Integral of $\frac{x}{9x^2-25}$ with respect to x

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Answer

$\frac{1}{18}\ln\left|9x^2-25\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x\:dx}{9x^2-25}$
1

Solve the integral $\int\frac{x}{9x^2-25}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=9x^2-25 \\ du=18xdx\end{matrix}$
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Isolate $dx$ in the previous equation

$\frac{du}{18x}=dx$

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Answer

$\frac{1}{18}\ln\left|9x^2-25\right|+C_0$