Evaluate: `intsin^4xcos^4x\ dx`

Explanation

`I=int sin ^{4} x cos ^{4} x d x `

`I=int(sin x cos x)^{4} d x`


Since,` sin 2 x=2 sin x cos x`

`Rightarrow I=frac{1}{16} int sin ^{4} 2 x d x `

`Rightarrow I=frac{1}{16} int(sin ^{2} 2 x)^{2} d x `

`Rightarrow I=frac{1}{16} int(frac{1-cos 4 x}{2})^{2} d x `

`Rightarrow I=frac{1}{64} int(1-2 cos 4 x+cos ^{2} 4 x) d x `

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