# How do you integrate x/(x^2+1)?

Nov 1, 2016

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

#### Explanation:

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

now $\frac{d}{\mathrm{dx}} \left({x}^{2} + 1\right) = 2 x$

so using $\int \frac{f ' \left(x\right)}{f \left(x\right)} = \ln | f \left(x\right) |$

we have $\int \left(\frac{x}{{x}^{2} + 1}\right) \mathrm{dx} = \frac{1}{2} \ln \left({x}^{2} + 1\right) + C$