Normalization of integral bounds

[Mr Davis 97]

Say we have a difficult integral of the form $\displaystyle \int_a^{b}f(x) ~dx$. Let $t = \frac{x-a}{b-x}$. Then $\displaystyle \int_0^{\infty}f \left( \frac{bt+a}{t+1} \right)\frac{1-a}{(t+1)^2} ~dt$. My idea is that making this change of variables transforms the integral into a form where we could potentially use the gamma function, Laplace transform, etc, to evaluate the integral. In practice is this not the case, and the integral just ends up getting messier?

 

[mathman]

Your last comment is correct. It will get messier most of the time.