# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

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

Learn how to solve integrals of rational functions problems step by step online. Integral of x/(x-5) with respect to x. Solve the integral \int\frac{x}{x-5}dx applying u-substitution. Let u and du be. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify. Split the fraction \frac{u+5}{u} inside the integral, in two terms with common denominator u.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 1.29 seconds