Calculus

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

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  1. 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?

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