Expert: Ahmed Salami - 2/5/2006

Question
What is the integral of:

e^ ((x^2)/2)

Answer
Hi John,
Sorry for the time it took.
Simple integration? I'm not sure i'll call it that.
There are some integrals that look simple enough but
cannot be solved using any of standard techniques used
in the rather elementary solutions. This is one example
of them, for it can only be solved using the method of
multiple integrals especially when we require a
definite integral, a topic in the more advanced study of
calculus. I don't know your level of mathematics and i
won't state that here.
But for the sake of saying something, you could try
integrating by series. By the Maclaurin's series(i hope
you've heard about it),
e^y = 1 + y + y^2/2! + y^3/3! + ..... + y^k/k!
where k! = k(k-1)(k-2)(k-3)........(3)(2)(1)
letting y = x^2/2
e^(x^2/2) = 1 + x^2/2 + x^4/4.2! + x^6/8.3! + ....... +
           x^2k/(2^k).k!
The integral would therefore be
x + x^3/6 + x^5/20.2! + x^7/56.3! + ......... +
x^(2k+1)/(2k+1)(2^k)k!

I hope i have helped, i'm open to discussions. You can always get back to me.
Regards.