Evaluate the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^7(\frac{x}{3})cos(\frac{x}{3}dx)$

Determine a change of variables from $x$ to $u.$ Choose the correct answer below.

A$.u=sinx$

B$.u=sin(\frac{x}{3})$

C$.u=si{n}^7(\frac{x}{3})$

D$.y=cos(\frac{x}{3})$

Write the integral in terms of $u.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^7(\frac{x}{3})cos(\frac{x}{3}dx)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}du$

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^7(\frac{x}{3})cos(\frac{x}{3}dx)=$

$$