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Step-by-step Solution

Integral of $\frac{x}{5-2x}$ with respect to x

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Answer

$\frac{1}{4}\left(5-2x\right)-\frac{5}{4}\ln\left|5-2x\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{xdx}{5-2x}$
1

Solve the integral $\int\frac{x}{5-2x}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=5-2x \\ du=-2dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{-2}=dx$

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Answer

$\frac{1}{4}\left(5-2x\right)-\frac{5}{4}\ln\left|5-2x\right|+C_0$