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

### Formulas

$-\ln\left|x\right|+arctan\left(x\right)+\frac{1}{2}\ln\left|1+x^2\right|+C_0$

## Step-by-step explanation

Problem

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

Using partial fraction decomposition, the fraction $\frac{x-1}{x\left(1+x^2\right)}$ can be rewritten as

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

$-\ln\left|x\right|+arctan\left(x\right)+\frac{1}{2}\ln\left|1+x^2\right|+C_0$

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

### Main topic:

Integrals by partial fraction expansion

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