Integrate the following

galactus · Oct 18, 2009, 02:17 PM

Yes, this is a toughy. It is not soable by elementary means. That is why parts and

Substitution would not work. Your professor probably meant $\int xe^{x}dx$

$\int\frac{e^{x}}{x}dx$

This has no closed form in elementary terms.

Over the yesrs mathematicians have came up with forms in order to represent things like this that are hard to deal with.

This one of yours is a form of the Exponential Integral, Ei(x), and can be represented by

$-Ei(1,-x)$

If you had limits, then we could probably evaluate. But an indefinite form is another matter.

Nhatkiem · Oct 18, 2009, 02:24 PM

Actually he meant x/e^x, which can be integrated by parts.

But thank you non-the-less, I think I'm going to read up some more about this Ei(x) form!

galactus · Oct 18, 2009, 02:26 PM

Just google the Exponential Integral. It is beyond elementary calculus and can be found in suh texts as Mathematical Physics.

$Ei(x)=\int_{x}^{\infty}\frac{e^{-t}}{t}dt$

One can find the asymptotic series for the expoenntial integral or express it as an Incomplete Gamma function.

Integrate the following

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