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# Integral of 1/(x(x-3))

### Videos

$\frac{1}{3}\ln\left|x-3\right|-\frac{1}{3}\ln\left|x\right|+C_0$

## Step-by-step explanation

Problem

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

Using partial fraction decomposition, the fraction $\frac{1}{x\left(x-3\right)}$ can be rewritten as

$\frac{1}{x\left(x-3\right)}=\frac{A}{x-3}+\frac{B}{x}$

$\frac{1}{3}\ln\left|x-3\right|-\frac{1}{3}\ln\left|x\right|+C_0$

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

### Main topic:

Integrals by partial fraction expansion

~ 0.38 seconds