integration of (e^(x^2))(dx)?

Answer 1

0.5 * (pi)^0.5 * erfi(x)

where erfi(x) is imaginary error function

Answer 2

this is very compicated, and is probable not worth doing ( i.e. you might be better off integrating numerically by using a calculator or MathCalc program). however if you must integrate abstractly, and assuming that you are only familiar with School calculus; here is how to tackle it
1) substitute p=x^2
2) find dp/dx
3) arrange to integrate by dp
4) you will need to integrate by parts (ignore constants of integration at this stage)
5) substitute x for p

i told you it wasn't worth doing!