With the substitution

u $=$ sin$($x$),$

we get

$15$ sin$2($x$)$ cos$($x$)$ dx

$=15$

u$2$ du$.$

which integrates to

$+$ C$.$

Substituting back in to get the answer in terms of sin$($x$),$ we have

$15$ sin$2($x$)$ cos$($x$)$ dx

$=$

$+$ C$.$