# What is the antiderivative of (5x)/(x^2+1)?

$\frac{5}{2} \setminus \ln \left({x}^{2} + 1\right) + C$

#### Explanation:

Given that

$\setminus \int \setminus \frac{5 x}{{x}^{2} + 1} \setminus \mathrm{dx}$

$= \frac{5}{2} \setminus \int \setminus \frac{2 x}{{x}^{2} + 1} \setminus \mathrm{dx}$

$= \frac{5}{2} \setminus \int \setminus \frac{d \left({x}^{2} + 1\right)}{{x}^{2} + 1}$

$= \frac{5}{2} \setminus \ln | {x}^{2} + 1 | + C$

$= \frac{5}{2} \setminus \ln \left({x}^{2} + 1\right) + C$