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# Integral of 1/(x^2(x+2))

### Videos

$\frac{1}{4}\ln\left|2+x\right|+\int\frac{\frac{1}{2}}{x^{2}}dx-\frac{1}{10}\ln\left|x\right|$

## Step-by-step explanation

Problem

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

Rewrite the fraction $\frac{1}{x^2\left(2+x\right)}$ using partial fraction decomposition as

$\frac{1}{x^2\left(2+x\right)}=\frac{A}{2+x}+\frac{B}{x^2}+\frac{C}{x}$

$\frac{1}{4}\ln\left|2+x\right|+\int\frac{\frac{1}{2}}{x^{2}}dx-\frac{1}{10}\ln\left|x\right|$

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

### Main topic:

Integrals by partial fraction expansion

~ 1.56 seconds