Textbook Problem

True or false: In evaluating ${\displaystyle \int udv}$ by parts,

(a) the parts u and dv are selected and the parts du and v are calculated.

(b) the differential (often dx) is always chosen as part of dv.

(c) the parts du and v are found from u and dv as follows:

$du=u\text{'}dx\text{ and }v= {\displaystyle \int dv}$

(d) For ${\displaystyle \int \frac{3x}{e^{2x}}}$ we could choose $u=3x$ and $dv=e^{2x}dx$.