I need help with this calc problem!!!!!?

Question

Intergrate (1-cos(t/2))^2 (sin(t/2))dt. where U = 1-cos(t/2)

I was using substitution, but i messed up along the way and i'm not getting the right answer. Please help. Thank you.

Answer 1

u = 1 - cos(t/2)

du = (1/2)sin(t/2) dt

sin(t/2) = 2du

int [2 u^2]

(2/3)u^3

(2/3) (1 - cos(t/2))^3 + C

Answer 2

set u=1-cos(t/2)

then du = 1/2 sin(t/2) dt or

dt=2 du/sin(t/2)

substitute these and the integral becomes:

u^2 sin(t/2) 2 du/sin(t/2) =

2u^2

this integrates to 2/3 u^3 = 2/3(1-cos(t/2)^3