October 3rd, 2018, 07:02 PM  #1 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,884 Thanks: 1088 Math Focus: Elementary mathematics and beyond  Challenge: integral
Challenge: $$\int\frac{x1}{x+x^2\log(x)}\,dx$$ 
October 3rd, 2018, 08:53 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,737 Thanks: 606 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: 19,951 Thanks: 1842 
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.

October 4th, 2018, 03:52 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,884 Thanks: 1088 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. 
October 4th, 2018, 04:34 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,951 Thanks: 1842 
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: 7,884 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
Why not?

October 4th, 2018, 07:29 PM  #8 
Senior Member Joined: Sep 2016 From: USA Posts: 520 Thanks: 293 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 5th, 2018, 12:08 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 19,951 Thanks: 1842  

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