integration of e ( to the power x-square)

Question

hoe to integrate - e to the power x square dx

Answer 1

e^x²=1+x²+x⁴/2!+...+∑x²ⁿ/n!+...

Therefore the integral of e^x² is C+x+x³/3+x⁵/10+...+∑x²ⁿ⁺¹/((2n+1)n!)+... expressed as an infinite power series, where C is a constant. 

(However, this integral is officially related to the Gauss error function usually given by erf(x) and the imaginary error function erfi(x). The constant multiplier √π/2 relates the integral to the error function.)