Integrating e^(t(x^2)): Mistakes, Confusion, and Solutions

[Tester_Boy]

not homework but stumbled across it when i was doing homework, turns out id made a mistake earlyer and didnt have to do it but still the fact sits that i didnt know how to do it wether i needed to at the time or not...
how do i intergrate

e^(t(x^2))

i know intergrating is the oposit of deferentiating so i started thinking, if i can find something that intergrates into it then i will have my answer. but the fact that it is e^x meens chain rule which meens the x in e^x will never change from x to x^2 as all powers of x in e^x stay the same. so i decided id have to start with e^(x^2) and realized this would always leave (x)e^(x^2) so I am truly confused about this i threw the t into check where constants go and what happens to them.
if i could get an explanation as well as the answer please many thanks =]

 

[qntty]

That particular antiderivative is not elementary. There are methods for finding anti derivatives which you will probably be learning very soon because it seems like you have just been introduced to them. They're basically the opposite of the rules for finding derivatives.

 

[Tester_Boy]

so how do you do that? =s

 

[NoMoreExams]

There's no closed form for $$\int e^{x^2} dx$$, obviously there's definite integral of it but for indefinite look up error function: http://en.wikipedia.org/wiki/Error_function