Evaluate: `int(sin8x)/(sqrt(9+sin^4 4x))dx`

Explanation

Let ` t=sin ^{2} 4 x`
`
d t=(2 sin 4 x cos 4 x) x(4 d x) `

we know `sin 2 x=2 sin 2 x cos 2 x`

Then, `d t=4 sin 8 x d x`

or `sin 8 x d x=d t / 4`
`

int frac{sin 8 x}{sqrt{9+sin ^{4} x}} d x=frac{1}{4} int frac{d t}{sqrt{3^{2}+t^{2}}}`


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