$\displaystyle \int\ cos^3xsin2x$

i first split up $\displaystyle cos^3x$ into $\displaystyle cosx(1-sin^2(x))$ and i said $\displaystyle sin2x= 2sinxcosx$. this is apparently the correct approach, but when i did it on my quiz today, i ended up getting $\displaystyle -1/10 cos^5x +c $instead of $\displaystyle -2/5 cos^5x +c $. the latter is the correct answer.. can someone help me find my mistake?