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Is it possible to integrate x^2*e^(x^2)?
Also, is it possible to integrate x*e^(x^2)?
If so, would you do it by parts?
Also, is it possible to integrate x*e^(x^2)?
If so, would you do it by parts?
Look at the solution and you'll see it contains a mystery function erfi(x). So what is this? It's a rabbit pulled out of the hat. This hat:JJacquelin said:
arildno said:the error function is a pesky, annoying rabbit jumping out of the hat, despite all the desperate attempts of mathematicians to keep them inside, or as second-best, make a nice coney stew out of it.
That pesky rabbit breeds too quickly to be constrained.arildno said:Rather, the error function is a pesky, annoying rabbit jumping out of the hat, despite all the desperate attempts of mathematicians to keep them inside, or as second-best, make a nice coney stew out of it.
Provable peskiness does not make the rabbits LESS pesky!meldraft said:Actually, it is possible to prove whether a function has an elementary antiderivative:
http://en.wikipedia.org/wiki/Liouville's_theorem_(differential_algebra)
I was hesitant at first about these pesky functions but I now know that these integrals have actually been proven not to have an elementary solution
Interesting point. I myself find it odd that "odd" has an odd number of letters too...meldraft said:Well, pesky is a word with an odd number of letters
Nature has a funny way of expressing itself (see attachment)
Yes, x^2*e^(x^2) can be integrated using basic integration techniques such as substitution, integration by parts, and partial fractions.
The general formula for integrating x^2*e^(x^2) is ∫ x^2*e^(x^2) dx = (1/2)e^(x^2) + C.
Yes, when integrating x^2*e^(x^2), if the limits of integration are from 0 to infinity, the integral converges to √π/4.
Yes, the integral of x^2*e^(x^2) can be represented graphically as a bell-shaped curve with the peak at (0,1/2) and asymptotes at x=±∞.
Yes, x^2*e^(x^2) can be integrated using numerical methods such as the trapezoidal rule, Simpson's rule, and Monte Carlo integration.