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

Explanation

I=`int(sin8x)/(sqrt(9+sin^4 4x))\ dx`

Suppose `t = sin^2 (4x)`

`dt = (2sin 4x cos 4x) x (4 dx)`

`dt = 4sin 8x dx `

or `sin 8x dx = dt/4`

So,

`I=1/4 int (dt)/(sqrt(3^2+t^2))`

`I=1/4 log(t+sqrt(t^2+3^2))+C`

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