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Find int (sin 2x cos 2x dx)/sqrt(9 - cos...

Find `int (sin 2x cos 2x dx)/sqrt(9 - cos^4(2x))`

Text Solution

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Let I = `int (sin 2x cos 2x dx)/sqrt(9 - cos^4(2x)) dx `
Put `cos^2(2x) = t` so that 4 sin 2x cos 2x dx = - dt
Therefore , I =`1/4 int -dt/sqrt(9 - t^2) = -1/4 sin^-1(t/3) + c = -1/4 sin^-1 [1/3 cos^2 2x] + c`
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