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Step-by-step Solution

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

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Answer

$x-5+5\ln\left|x-5\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{x}{x-5}\right)dx$
1

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

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

Rewriting $x$ in terms of $u$

$x=u+5$

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Answer

$x-5+5\ln\left|x-5\right|+C_0$
$\int\left(\frac{x}{x-5}\right)dx$

Main topic:

Integrals of Rational Functions

Used formulas:

5. See formulas

Time to solve it:

~ 0.76 seconds

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