My Math Forum Challenge: integral

 Calculus Calculus Math Forum

 October 3rd, 2018, 07:02 PM #1 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,913 Thanks: 1112 Math Focus: Elementary mathematics and beyond Challenge: integral Challenge: $$\int\frac{x-1}{x+x^2\log(x)}\,dx$$
 October 3rd, 2018, 08:53 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,765 Thanks: 623 Math Focus: Yet to find out. Is it $b \tan^{-1}(x) + C$ for real b?
 October 3rd, 2018, 09:37 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,301 Thanks: 1971 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. Thanks from greg1313 and Joppy
 October 3rd, 2018, 10:39 PM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,765 Thanks: 623 Math Focus: Yet to find out. Would someone like to start a thread like this one? i.e. post a challenging integral, whoever solves it posts another and so on. Thanks from greg1313
 October 4th, 2018, 03:52 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,913 Thanks: 1112 Math Focus: Elementary mathematics and beyond I'm in. If skipjack's in, he can post the next one. If not, it's your turn, Joppy. Thanks from Joppy
 October 4th, 2018, 04:34 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,301 Thanks: 1971 This isn't a good idea.
 October 4th, 2018, 07:23 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,913 Thanks: 1112 Math Focus: Elementary mathematics and beyond Why not?
 October 4th, 2018, 07:29 PM #8 Senior Member   Joined: Sep 2016 From: USA Posts: 559 Thanks: 324 Math Focus: Dynamical systems, analytic function theory, numerics This seems like fun. It can't be less fun than reading about yet another disproof of Cantor or RH proof.
 October 4th, 2018, 07:43 PM #9 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,765 Thanks: 623 Math Focus: Yet to find out. Started a new thread here so it's clear for everyone.
October 5th, 2018, 12:08 AM   #10
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Quote:
 Originally Posted by greg1313 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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