TITLE: How to evaluate this integral with $\sin$ and $\cos$?
QUESTION [5 upvotes]: $$ \int \sin^6 x\cos^4x\ dx$$
I have absolutely no idea how to solve it. I tried to use formula of degree reduction but failed. Help me please. Thank you.

REPLY [3 votes]: HINT:
If you are allowed to  use Euler Formula,
$\displaystyle\sin x=\frac{e^{ix}-e^{-ix}}{2i}$ and $\displaystyle\cos x=\frac{e^{ix}+e^{-ix}}2$
and use Binomial Expansion