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Step-by-step Solution

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

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Answer

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

Step-by-step explanation

Problem to solve:

$\int\frac{3}{x^2+3x}dx\:$
1

Factoring by $x$

$\int\frac{3}{x\left(x+3\right)}dx$
2

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

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

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Answer

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