[hyperbovine]

It's going to take you a while to numerically solve that integral for the uncountably many values of \alpha that you are being asked to...

[benlivengood]

It's probably best to return a function that takes alpha as a parameter and numerically integrates for whichever finite set of alphas are required by the caller.

[fooker]

The usual method is to computer a reasonable number of solutions and do curve fitting.

[Kranar]

It's the algorithm in and of itself that serves as the solution to the integral.