# Math Help - trig integral

1. ## trig integral

$\int\ cos^3xsin2x$

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

2. convert sin(2x) into 2sin(x)cos(x) and then you should be ready to integrate using the power rule with u substitution where u = cos(x)