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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
7 months, 1 week 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 · 7 months, 1 week ago

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@Hummus A Ah, cool, thanks Hummus! I'll take a look at it when I get a chance! Geoff Pilling · 7 months, 1 week ago

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just use the expansion for ln x and integrate and have an approx result. As Asd · 7 months, 1 week ago

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