# How do you find the indefinite integral of int root3(7v)dv?

##### 1 Answer
Aug 29, 2017

The integral equals $\frac{3}{28} {\left(7 v\right)}^{\frac{4}{3}} + C$

#### Explanation:

We let $u = 7 v$. Then $\mathrm{du} = 7 \mathrm{dv}$ and $\left(\mathrm{dv}\right) = \frac{\mathrm{du}}{7}$.

$I = \int \sqrt[3]{u} \cdot \frac{\mathrm{du}}{7}$

$I = \frac{1}{7} \int \sqrt[3]{u} \mathrm{du}$

$I = \frac{1}{7} \int {u}^{\frac{1}{3}} \mathrm{du}$

$I = \frac{1}{7} \left(\frac{3}{4} {u}^{\frac{4}{3}}\right) + C$

$I = \frac{3}{28} {\left(7 v\right)}^{\frac{4}{3}} + C$

Hopefully this helps!