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October 3rd, 2018, 07:02 PM   #1
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Challenge: integral

Challenge:

$$\int\frac{x-1}{x+x^2\log(x)}\,dx$$
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October 3rd, 2018, 08:53 PM   #2
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Is it $b \tan^{-1}(x) + C$ for real b?
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October 3rd, 2018, 09:37 PM   #3
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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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October 3rd, 2018, 10:39 PM   #4
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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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October 4th, 2018, 03:52 PM   #5
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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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October 4th, 2018, 04:34 PM   #6
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This isn't a good idea.
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October 4th, 2018, 07:23 PM   #7
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Why not?
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October 4th, 2018, 07:29 PM   #8
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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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October 4th, 2018, 07:43 PM   #9
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Started a new thread here so it's clear for everyone.
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October 5th, 2018, 12:08 AM   #10
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Quote:
Originally Posted by greg1313 View Post
Why not?
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.
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