just do successive integrations by parts (2).
Hi. You can integrate right? Just let and and then keep re-integrating by parts until you reduce the power on x to one.
Above, you have right? Surely you can take the second derivative to obtain . Now, that's no problem to square it and then expand out all the terms. You'll end up with terms like , and which you can then integrate by parts like above and solve.
And Moo forgot the product rule of differentiation
But basically for each term of the integral, you need at most 2 integrations by parts. And since there are 3 of them, that's surely not a very nice thing to do.
I'm thinking on a probabilistic way of solving it, but I can't seem to find it.
How did you come up with this integral ?
Well thanks for that! Could you just tell me why the bound of the integral changes from -infinity to zero on the second line and on the third line how you go from u to gamma and what happens to the e^-u, also could you tell me how you get from the part with the gammas in to the answer. Thanks very much.