Evaluating $\int(2x^2+1)e^{x^2}dx$ $$\int(2x^2+1)e^{x^2}dx$$
The answer of course:
$$\int(2x^2+1)e^{x^2}\,dx=xe^{x^2}+C$$
But what kind of techniques we should use with problem like this ?

As @Peter note above, you can integrate this by separating the integrand and integrating by parts: \begin{align} \int(2x^2+1)e^{x^2}dx &=\int2x^2e^{x^2}dx+\int e^{x^2}dx\\ &=\int x(2xe^{x^2})dx+\int e^{x^2}dx\\ &= \int x\left(\frac{d}{dx}e^{x^2}\right)dx\ + \int e^{x^2}dx\\ &= xe^{x^2}-\int e^{x^2}dx+ \int e^{x^2}dx= xe^{x^2} + C \end{align}
