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Tough Integral

This integral has always eluded me:

\[ \large \int e^{x} \ln(x) \, dx \]

Does anyone know the general solution to it?

Note by Geoff Pilling
1 year, 6 months ago

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well,this can't be done until you introduce something called the exponential integral,you can read about it here,which doesn't have a closed form most of the time

the solution to the integral above is \[e^x\ln(x)-\text{Ei}(x)\]

where \(\text{Ei}\) denotes the exponential integral

Hummus A - 1 year, 6 months ago

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Ah, cool, thanks Hummus! I'll take a look at it when I get a chance!

Geoff Pilling - 1 year, 6 months ago

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just use the expansion for ln x and integrate and have an approx result.

As Asd - 1 year, 6 months ago

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