Evaluate: `intxcos^3x\ dx`

Explanation

`int x cos ^{3} x d x`
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x int cos ^{3} x-int frac{d}{d x} int cos ^{3} x d x`
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int cos ^{3} x d x=int(cos x-sin ^{2} x cos x) d x`
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sin x-frac{sin ^{3} x}{3}`
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x sin x-frac{x sin ^{3} x}{3}-int(sin x-frac{sin ^{3} x}{3}) d x`
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x sin x-frac{x sin ^{3} x}{3}-frac{cos ^{3} x}{9}+frac{8 cos x}{9}`
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