I have an integral here that I'm trying to figure out.
$$ \int 7\sin^2x \cos^4x\ dx $$
Here's what I got as an answer:
$$ \frac{7}{16}x-\frac{7}{64}\sin4x+\frac{7}{12}\sin2x + C $$
However, I'm doubting myself and the check didn't seem to produce good results. I can give some steps if you want. I filled a whole page with work, and it seems like it should be easier than that. Any ideas?