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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 realised this would always leave (x)e^(x^2) so im truly confused about this i threw the t in to check where constants go and what happens to them.

if i could get an explination as well as the answer please many thanks =]