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Let \[S=\sum_{r=1}^{\infty} \int_{-\infty}^{\infty}\frac{dx}{x^2-2^{(2^{(r+1)})}x+3^r}\]

Then find, \(S^3+9S+27\)

Note: Work with the Cauchy principal value of the integrals.

If you're looking for another challenge in calculus, try this

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