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Step-by-step Solution

Integral of $\frac{5x}{5x^2+10}$ with respect to x

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Answer

$\frac{1}{2}\ln\left|5x^2+10\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{5x}{5x^2+10}\right)dx$
1

Taking the constant out of the integral

$5\int\frac{x}{5x^2+10}dx$
2

Solve the integral $\int\frac{x}{5x^2+10}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=5x^2+10 \\ du=10xdx\end{matrix}$

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Answer

$\frac{1}{2}\ln\left|5x^2+10\right|+C_0$
$\int\left(\frac{5x}{5x^2+10}\right)dx$

Main topic:

Integrals of Rational Functions

Used formulas:

4. See formulas

Time to solve it:

~ 0.84 seconds