Textbook Problem

In Problems 25-30, select the formula or method (I-IV) that should be used to evaluate each integral. Then evaluate the integral.

Integration by parts

II. ${\displaystyle \int e^{u}du}$

III. ${\displaystyle \int \frac{du}{u}}$

IV. ${\displaystyle \int u^{n}du}$

${\displaystyle \int x{e}^{x^2}}dx$