Evaluate (Integral) sin 4x cos^2 4x dx.

A. Cos^3(4x)/3 + C
B. -Cos^3(4x)/3 + C
C. Cos^3(4x)/12 + C
D. -Cos^3(4x)/12 + C

1 answer

Use the substitution
p=cos(4x)
dp=-4sin(4x)dx
I=∫sin(4x)cos²(4x)dx
=∫(1/4)p²dp

Can you take it from here?