# Step-by-step Solution

## Integral of $\frac{3}{x^2+3x}$ with respect to x

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### Videos

$\ln\left|x\right|-\ln\left|x+3\right|+C_0$

## Step-by-step explanation

Problem to solve:

$\int\frac{3}{x^2+3x}dx\:$
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Factoring by $x$

$\int\frac{3}{x\left(x+3\right)}dx$
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Rewrite the fraction $\frac{3}{x\left(x+3\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{3}{x\left(x+3\right)}=\frac{A}{x}+\frac{B}{x+3}$

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

### Main topic:

Integrals of Rational Functions

~ 0.91 seconds