This integral poses a challenge.
Ordinarily integrating rational functions can be solved using the Hermite-Ostrogradski method. However, in the following integral, the coefficients are not integers. (Hence, the Hermite-Ostrogradski method would not be appropriate).
Note: Expanding the integrand (trying to solve the integral using a partial fraction decomposition) is (because of the nature of the physical problem described by this integral) an inappropriate solution to this case.
How can this rational function be evaluated?