I hit a wall with this problem: $\int_2^3 \sin x (\cos 2x)^4 \,\text{d}x$. Clearly, I can use the double angle equation, expand, distribute, and integrate each piece; but the problem set is supposed to use substitution. I cannot find the right substitution. What am I missing? Thanks.
2026-03-30 15:14:08.1774883648
Double angle substitution in $\int_2^3 \sin x (\cos 2x)^4 \,\text{d}x$
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HINT:
As $\int\sin x\ dx=-\cos x,$
use $\cos2x=2\cos^2x-1$ and set $\cos x=u$