MHB Integral: Investigating Convergence II

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The discussion focuses on investigating the convergence of the integral $\int_{0}^{\infty} \frac{x^{ \frac{2}{3}} + \frac{2}{3} \ln x }{1+x^2} \mbox{d}x$. Participants are encouraged to share their progress or initial thoughts to facilitate more effective assistance. The emphasis is on collaborative problem-solving, ensuring that helpers can provide relevant guidance based on the user's current understanding. The conversation highlights the importance of demonstrating prior work to avoid redundant suggestions. Overall, the thread aims to deepen the understanding of this specific integral's convergence.
maxkor
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Investigate the convergence of the integral
$\int_{0}^{\infty} \frac{x^{ \frac{2}{3}} + \frac{2}{3} \ln x }{1+x^2} \mbox{d}x$
 
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Hello and welcome to MHB, maxkor! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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