How can I find the integral of: sin^6 of theta cos^6 of theta dtheta?

I tried u substitution however, I can't seem to be able to get rid of the exponent

Question

How can I find the integral of: sin^6 of theta cos^6 of theta dtheta?

I tried u substitution however, I can't seem to be able to get rid of the exponent

issy14 · Answer

$$\int\limits_{?}^{?} \sin^6(\theta) \cos(\theta) d \theta $$

issy14 · Answer

It's not a definite integral.

anonymous · Answer

use trig identities

issy14 · Answer

I tried, to use them but I can't get rid of the exponent

anonymous · Answer

Do you mean
$$\large\int\sin^6\theta\cos^6\theta~d\theta$$
like you said in your first post, or
$$\large\int\sin^6\theta\cos\theta~d\theta~~?$$

anonymous · Answer

hi there...you need to use a Reduction formula...it's too complex to solve by traditional means... I would suggest searching youtube for reduction formula integration... if you want to see what these look like, click here...they are crazy! good luck! http://archives.math.utk.edu/visual.calculus/4/recursion.2/ you can watch this similar problem as well>>> https://www.youtube.com/watch?v=hV5af_07ToE :o)