What is the antiderivative of (1-cos(t/6))^3 * sin(t/6)?

[cemar.]

Hey guys!
So i have to find the antiderivative of
(1-cos(t/6))^3 * sin(t/6)
I have tried a bunch of different ways like by parts, trig substitution, identities, u-substitution then developing it, etc. but i just can't get it!
Can some one just tell me the proper method to use after that I am sure i can figure it out.
thanks!

 

[Dick]

You must not have tried u substitution very hard. Try u=(1-cos(t/6)).

 

[Defennder]

It should be doable. Or so says Wolfram's online integrator. I tried it out and managed to reduce it to a doable trigo form. You only need use integration by parts and then replace all those trig terms which are of power 2 and 3 with power 1 terms by means of some trigo formulae.

 

[Dick]

It should be doable. Or so says Wolfram's online integrator. I tried it out and managed to reduce it to a doable trigo form. You only need use integration by parts and then replace all those trig terms which are of power 2 and 3 with power 1 terms by means of some trigo formulae.

I don't see why you are working so hard on it. There's a much simpler way.

 

[Defennder]

You're right, I just didn't see it before you posted.