Note: You can get full credit for this problem by just entering the answer to the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the indefinite integral $\displaystyle \int \cos^{13}(7 t)\sin(7 t)\, dt$
Then the most appropriate substitution to simplify this integral is
$u$ = Then $dt = f(t)\,du$ where
$f(t)$ =

After making the substitution we obtain the integral $\displaystyle \int g(u)\,du$ where
$g(u)$ =

This last integral is: = $+ C$
After substituting back for $u$ we obtain the following final form of the answer:
= $+ C$