What is the value of the Cosine integral \begin{align} \int_{0}^{\infty} \cos\left( \frac{x (x^{2}-a^{2})}{x^{2}-b^{2}} \right) \, \frac{dx}{x^{2} + p^{2}} \, \, \, ? \end{align}
2026-04-03 17:26:37.1775237197
A Cosine Integral
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$$\frac{\pi}{2p} \exp\left[-p\frac{a^2+p^2}{b^2+p^2}\right]$$
This was submitted as a problem to the Gazette of the Royal Math. Soc. of Spain and is still open, so the solution will not be given here. Methods for the general class of integrals of this sort will be found in the book (in preparation) ``Fun With Integrals" (Borwein and Glasser)