Question

integral of e^(x^2)(2x^2+1)

Answer 1

i tried substitution x^2=u ... and it seems that it could work but i'm not quite there yet

Answer 2

i don't know how to solve this with substitution but intuitively:
let f(x) = e^(x^2)
f'(x) = 2xe^(x^2)

integral becomes f'(x)*x + f(x)
this looks like product rule for derivatives
d/dx x*f(x) = f'(x)*x + f(x)

therefore anti-derivative is x*e^(x^2) +c

Answer 3

WOW !!! very elegant solution !!! =]

Answer 4

thanks

here is solution via wolfram
http://www.wolframalpha.com/input/?i=integrate+%282x^2+%2B1%29e^%28x^2%29+dx
notice it doesn't show any steps...