# Math Help - trigonometric integrals

1. ## trigonometric integrals

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.

2. let $t = \frac{x}{2}$

$dt = \frac{1}{2} \, dx$

$dx = 2 \, dt$

$\int \sin^5\left(\frac{x}{2}\right) \, dx$

$\int \sin^5(t) \cdot 2 \, dt$

$2 \int \sin^5(t) \, dt$

now do the integration