What is ∫ (4sin 8x)/(√(1-cos^4 4x))dx?

$I+\int\frac{sin8x}{\sqrt{1-cos^44x}}dx$

Let $\cos^2 4x=t$.

Differentiating,

$dt=(2cos4x).(-4sin4x) dx$

$dt=-4sin8xdx$.....(1)

$I+\int-\frac{1}{4}.\frac{dt}{\sqrt{1-t^2}}$

$=-\frac{1}{4}.sin^{-1}(t)+C$

$=-\frac{1}{4}sin^{-1}(cos^24x)+C$