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How do I solve the following definite integral (preferably by an asymptotic method)?

$$ \int_{1}^{\infty} \frac{\sin^2 (\mu \sqrt{x^2 -1})}{(x+1)^{\frac{9}{2}} (x-1)^{\frac{3}{2}}} \,dx $$ Note: $\mu$ here is an extremely small constant. I have tried: Estimating the integral by Tay …
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