# Homework Help: Integrate e^x^2, using Maclaurin rule.

1. Feb 9, 2014

### Jarfi

1. The problem statement, all variables and given/known data

I am suppost to integrate e^x^2 from 0 to 1 and such, I using Maclaurins rule, I got e^x=1+x/1!+x^2/2!+...+x^n/n!+e^(öx)*x^n+1/(n+1)!, 0<ö<1.

But when I put in x^2 instead of x, I end up with a legit thing except e^(öx^2)x^n+1/(n+1)! and this is giving me e^x^2 again!

2. Feb 9, 2014

### dextercioby

Why don't you compute the whole series for e^(x^2) using the generic Mac-Laurin series ?

3. Feb 9, 2014

### Jarfi

would take eons, gotta give the project in before 8 am morning ! anyways I figured it out, writing the "leftover" part using some rule that allowed me to take the e^ö^x^2 outside the integral.

4. Feb 9, 2014

### Staff: Mentor

No, it wouldn't take "eons". Just replace x with x2 in the Maclaurin expansion for ex. It could be you're thinking you have to take a bunch of derivatives - not so.
First off, I don't know what e^ö^x^2 is supposed to be, especially with what renders for me as an o with an umlaut.
Second, if you're integrating a function of x, you can't just pull out a factor that has x in it.