The integral $\int \frac{2 x+x^3}{1+x^2} dx$ is equal to:

$\log \left(1+x^2\right)+x+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+x^2+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+\frac{1}{2} x+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration

$\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration

The correct answer is Option (4) → $\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration