Challenge: integral

greg1313

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Oct 2008
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Challenge:

$$\int\frac{x-1}{x+x^2\log(x)}\,dx$$
 
Feb 2016
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Is it $b \tan^{-1}(x) + C$ for real b?
 

skipjack

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For $x$ > 0, \(\displaystyle \!\int\! \frac{x - 1}{x + x^2\ln(x)}\,dx = \!\int\!\left(\frac{1 + \ln(x)}{1 + x\ln(x)} - \frac{1}{x}\right)dx = \ln(1 + x\ln(x)) - \ln(x) + \mbox{C}\), where $\mbox{C}$ is a constant.
 
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Would someone like to start a thread like this one?

i.e. post a challenging integral, whoever solves it posts another and so on.
 
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greg1313

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I'm in. If skipjack's in, he can post the next one. If not, it's your turn, Joppy. :)
 
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skipjack

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This isn't a good idea.
 

greg1313

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Why not?
 

SDK

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This seems like fun. It can't be less fun than reading about yet another disproof of Cantor or RH proof.
 
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Started a new thread here so it's clear for everyone.
 

skipjack

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It's very time-consuming and all the straightforward examples can be done by WolframAlpha.

Also, it encourages integrals to be posted where the result happens to be much more complicated than the integrand. These are often more tedious than interesting.