Consider the following.

sin$3($y$)$ cos$6($y$)$ dy

This is an integral of the form

$$sinm$($y$)$ cosn$($y$)$ dy$,$

where the power of sine is $---$Select$---$odd$$even and the power of cosine is $---$Select$---$odd$$even $.$ The strategy for evaluating an integral of this type is to save one $---$Select$---$sine$$cosine factor and use

sin$2($x$)=1$ cos$2($x$)$

to express the remaining factors in terms of $---$Select$---$sine$$cosine $.$ Then, use the following substitution.

u $=$

$1$cos$3($y$)$

Evaluate the integral. $($Use C for the constant of integration.$)$