Find the integrals of the functions \( \sin 4 x \sin 8 x \) \( \int...

Find the integrals of the functions \( \sin 4 x \sin 8 x \)
\( \int \sin 4 x \cdot \sin 8 x d x=\frac{1}{2} \int 2 \sin 4 x \cdot \sin 8 x d x \)
\[
2 \sin A \sin B=\cos (A-B)-\cos (A+B)
\]
\[
=\frac{1}{2} \int \cos C
\]