The functions $\displaystyle y=e^{x^2}$ and $\displaystyle y=x^2 e^{x^2}$ don't have elementary antiderivatives, but $\displaystyle y=(2x^2+1) e^{x^2}$ does. Evaluate $$\int {(2x^2+1) e^{x^2}}\, dx$$

Note: Use an upper-case "C" for the constant of integration.