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Deriving the (open-form) integral of e^(x^2)

WARNING: Math content ahead!

Although e^(x^2) does not have an antiderivative that can be written finitely as a bunch of elementary functions smooshed together (aka a closed-form antiderivative), it DOES have an open-form antiderivative. This derivation starts with the power series for e^x, and substitutes in x^2 for x, yielding the power series for e^(x^2). This can be integrated term by term, yielding the power series form of the most general antiderivative of e^(x^2).

yeah so about how i have no fucking algebraic idea at how to take the antiderivative of something thats inside a radical.

one number, i can deal with. but a whole little equation

no

fuck

what? how?

I DO NOT UNDERSTAND DIFFERENTIAL EQUATIONS.

ok so the lecturer was using y’ = y^4 - y^2 as an example. he did a slope field and all that stuff. but like. can’t you just take the antiderivative of that function? i don’t understand where the slope field and all the solutions derived from the slope field come from. shouldn’t the solutions just be 1/3y^3 - y + C? but with the slope field he’s getting all sorts of different solutions that aren’t accounted for by adding C.

i guess it doesn’t really matter right now since i’m not actually taking differential equations yet, but lol. it’d be nice to be able to watch this lecture series. altho perhaps i should finish the one on infinite series first since i’m actually taking that class in a couple weeks…

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