# How do I evaluate int5v (v^2 + 2)^2dv?

I would use a Brute Force approach, expanding the square, multiplying by $5 v$ and integrating:
$\int 5 v {\left({v}^{2} + 2\right)}^{2} \mathrm{dv} = \int 5 v \left({v}^{4} + 4 {v}^{2} + 4\right) \mathrm{dv} =$
$\int \left(5 {v}^{5} + 20 {v}^{3} + 20 v\right) \mathrm{dv} = 5 {v}^{6} / 6 + 20 {v}^{4} / 4 + 20 {v}^{2} / 2 + c =$
$= \frac{5}{6} {v}^{6} + 5 {v}^{4} + 10 {v}^{2} + c$
Remember that $\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + c$