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Step-by-step Solution

Integral of x/((x-3)^2)

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Answer

$\ln\left|x-3\right|+\frac{-3}{x-3}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x}{\left(x-3\right)^2}dx$
1

Solve the integral $\int\frac{x}{\left(x-3\right)^2}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x-3 \\ du=dx\end{matrix}$
2

Rewriting $x$ in terms of $u$

$x=u+3$

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Answer

$\ln\left|x-3\right|+\frac{-3}{x-3}+C_0$
$\int\frac{x}{\left(x-3\right)^2}dx$

Main topic:

Integration by substitution

Used formulas:

6. See formulas

Time to solve it:

~ 1.36 seconds

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