i need some help with what to do when there is something inside the trig function.

so this problem is:

sin(x/2)^5

i could do it, i think, if it were just sin(x). but not completely sure what to do now.

so i change it to:

(sin(x/2)^2)^2 *(sin(x/2)). which changes to

(1-cos(x/2)^2)^2 *(-d(cosx). then

(1-u^2)^2 *(-du)

but what do i do with the inside part of this? can someone explain it or show me to solve the rest of it? or tell me what i've done wrong so far. i don't want to go through solving the rest of it because i don't know what exactly to do.