This is neat, I think I can learn this trick. Just one question, when you substituted

you didn't do anything to the lower bound of integral which was

- instead, you put it zero. Is it legitimate? Since the lower bound was y, and the new variable of integration (u) still depends on y, why did you change it to zero just like that?

(Also, isn't it strange that

and

both equal to the same number, 1? understand that this comes from

and that 0!=1 by convention, but I still find it very strange.)

By the way, I did another (non-Gamma) integration but with some substition and I got to

which is still not correct. But I'll rechecked my signs and I still cannot figure out where I make mistake. I'll keep trying, binomially, until success...