Bangz
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This integral does not have antiderivative that is elementary. However, when I attempted it (before knowing the functions nature) I was able to get an elementary antiderivative. Which tells me something in my method must be wrong?

My working is below. Apologies for the handwriting.
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Bangz
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Sir Cumference
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(Original post by Bangz)
This integral does not have antiderivative that is elementary. However, when I attempted it (before knowing the functions nature) I was able to get an elementary antiderivative. Which tells me something in my method must be wrong?

My working is below. Apologies for the handwriting.
After a quick look I can't see how you've arrived at this

\displaystyle \int xe^x(\ln x - 1) \ dx = e^x - \int e^x + \frac{e^x}{x} \ dx

Can you explain it please?
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Bangz
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(Original post by Notnek)
After a quick look I can't see how you've arrived at this

\displaystyle \int xe^x(\ln x - 1) \ dx = e^x - \int e^x + \frac{e^x}{x} \ dx

Can you explain it please?
Via integration by parts. I let U be xe^x and my dV be lnx - 1
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Sir Cumference
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Bangz I can see that your IBP explanation is below the working (which is confusing!). I'll have another look.
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RDKGames
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(Original post by Bangz)
Via integration by parts. I let U be xe^x and my dV be lnx - 1
Surely it's not that.

You differentiated the entire thing for some reason instead of integrating it.

dv/dx becomes v through integration, but ln(x)-1 becomes 1/x through differentiation...

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Bangz
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(Original post by RDKGames)
Surely it's not that.

You differentiated the entire thing for some reason instead of integrating it.

Aaaah thanks. Stupid mistake.
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Sir Cumference
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Too slow

Bangz try to make sure your working is consistent, especially when showing it to someone else. Your "Let u(x) = ..." sometimes appeared above the IBP and sometimes below which was very confusing!
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Bangz
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(Original post by Notnek)
Too slow

Bangz try to make sure your working is consistent, especially when showing it to someone else. Your "Let u(x) = ..." sometimes appeared above the IBP and sometimes below which was very confusing!
Sorry about that
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