Can someone help me to regularize the following divergent integral?
$ \int_0^{1/2}\, \frac{d x}{x^{3/2} (1-x)^{3/2}} $
Guys, thank you very much for your answers. Thus if I have understood your procedure, the regularized result of this divergent integral (let's do a trivial case) $ \int_0^\infty{dx} = \lim_{\Lambda\rightarrow \infty} \int_0^\Lambda{dx}=\lim_{\Lambda\rightarrow \infty}\Lambda - 0 \equiv 0 $ is zero because one simply remove the divergency and the game is over, right?
Well, I would like to have your opinion about this other regularization I have thought of $ \int_0^\infty{dx} = \lim_{m\rightarrow\infty} \int_0^m{dx} = \lim_{m\rightarrow\infty} 1+\sum_{n=1}^{m-1} 1 = \lim_{m\rightarrow\infty} 1+\sum_{n=1}^{m-1} {1\over n^0} = 1+\zeta(0)=1-{1\over 2}={1\over 2} $ where I have used the well-known value $\zeta(0)=-1/2$ of the Riemann $\zeta$-function. I was wondering what can be the physical interpretation of such a (naive, I admit) regularization...but maybe there is none and I am just a crazy physicist :)