Find the following integral: $\int(2x^{2}+e^{x})dx$

To find the integral $\int(2x^{2}+e^{x})dx$,we use the linearity property of integration:
$\int(2x^{2}+e^{x})dx = 2\int x^{2}dx + \int e^{x}dx$
Using the power rule $\int x^{n}dx = \frac{x^{n+1}}{n+1} + C$ and the exponential rule $\int e^{x}dx = e^{x} + C$:
$= 2\left(\frac{x^{3}}{3}\right) + e^{x} + C$
$= \frac{2}{3}x^{3} + e^{x} + C$
where $C$ is an arbitrary constant.