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If ∫0∞sin3xx3dx = A\large \displaystyle \int_{0}^{\infty} \dfrac{\sin^3 x}{x^3} dx \ = \ A ∫0∞x3sin3xdx = A and ∫0∞(x−sinxx3)dx = mAn\large \displaystyle \int_{0}^{\infty} \left (\dfrac{x - \sin x}{x^3} \right ) dx \ = \ \dfrac{m A}{n} ∫0∞(x3x−sinx)dx = nmA where mmm and nnn are positive relative coprimes, then what is m+nm+n m+n?.
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