The Attempt at a Solution
I don't even know where to start , I either got to do this by basic substitution or by parts. Basic substitution doesn't help for obvious reasons, so I thought I'd do it by parts, but that would get completely messed up based upon the e^x^2 not having any anti-derivative, so I'd need basic substitution to get rid of it.
I thought of making:
u = e^x^2
ln|u| = x^2
√ln|u| = x
du = 2xe^x^2 dx
Therefore, my equation would be:
(2ln|u| + 1)/(2√[ln|u|]) du
Then I thought about breaking that up:
integrate: (2ln|u|)/(2√[ln|u|]) + 1/(2√[ln|u|])
(ln|u|)/(√[ln|u|]) + 1/(2√[ln|u|])
Annnndd... now I'm stuck again because that square root is basically the most evilest thing on the entire planet. It limits partial fractions, I can't exactly do trig substitution, and the fraction kills by parts.