Integral of $$$\frac{2 x - 1}{\left(x + 2\right) \left(x^{2} + 1\right)^{2}}$$$

The calculator will find the integral/antiderivative of $$$\frac{2 x - 1}{\left(x + 2\right) \left(x^{2} + 1\right)^{2}}$$$, with steps shown.

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