I did it using substitution

firts, make a=-x^2

now, da=-2x dx

now the integral looks like:

-(1/2) [Integral] e^a da

and just integrate, with the answer being:

-(1/2) e^a + C

and substitute back

-(1/2) e^(-x^2) + C

I think that's about right.

PS. [Integra] is the integral sign