My Math Forum Challenge: integral

 Calculus Calculus Math Forum

 October 3rd, 2018, 06:02 PM #1 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Challenge: integral Challenge: $$\int\frac{x-1}{x+x^2\log(x)}\,dx$$
 October 3rd, 2018, 07:53 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 Math Focus: Yet to find out. Is it $b \tan^{-1}(x) + C$ for real b?
 October 3rd, 2018, 08:37 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,935 Thanks: 2209 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, 09:39 PM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 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, 02:52 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 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, 03:34 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,935 Thanks: 2209 This isn't a good idea.
 October 4th, 2018, 06:23 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Why not?
 October 4th, 2018, 06:29 PM #8 Senior Member   Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 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, 06:43 PM #9 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 Math Focus: Yet to find out. Started a new thread here so it's clear for everyone.
October 4th, 2018, 11:08 PM   #10
Global Moderator

Joined: Dec 2006

Posts: 20,935
Thanks: 2209

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.

 Tags challenge, integral

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Math Message Board tutor Calculus 0 August 29th, 2016 07:45 AM Etyucan Real Analysis 8 March 19th, 2013 05:49 AM Etyucan Real Analysis 5 March 7th, 2013 07:41 PM Etyucan Real Analysis 7 February 20th, 2013 10:40 AM NOJEA Computer Science 1 November 3rd, 2012 11:06 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top