Question

Find the integral of (sin^4(x))(cos^4(x)) dx

Answer 1

\[\sin^4(x) \cos^4(x) \\ =(\sin(x) \cos(x))^4=(\frac{1}{2} \sin(2x))^4=\frac{1}{2^4} \sin^4(2x) \\ =\frac{1}{16} \sin^4(2x)=\frac{1}{16} (\sin^2(2x))^2 \\ =\frac{1}{16} (\frac{1-\cos(4x)}{2})^2 \\ =\frac{1}{16} \cdot \frac{1}{4} (1-\cos(4x))^2 \\ =\frac{1}{64}(1-2 \cos(4x)+\cos^2(4x))\]
use one more power-reducing formula and it should be in a form that is easy to integrate after that

Answer 2

ahh okay thank you, let me see what I get