Answer
$ \displaystyle \frac{(3x+1)^{6}}{18}+C$
Work Step by Step
see Substitution RuIe, p.962:
(1)
let $u=3x+1$
(2)
$du=3dx\displaystyle \ \ \Rightarrow\ \ dx=\frac{du}{3}$
$(3)$
$\displaystyle \int(3x+1)^{5}dx=\int u^{5}(\frac{du}{3})$
... constant multiple, power rules
$= \displaystyle \frac{1}{3}\cdot\frac{u^{6}}{6}+C$= ... bring back x
$=\displaystyle \frac{(3x+1)^{6}}{18}+C$
