Meden Agan's latest activity
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with
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The logarithm was obtained from WA. The entire calculation will follow. I think I made an error. Let me check this first. -
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.All correct, as far as I'm concerned. Previously, I got confused because I had the variables ##y## and ##z## interchanged. Now, do you...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I made a mistake and corrected it. That simplifies the formulas a bit. Integration by parts with ##\operatorname{arsinh}## has always...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
Ignoring the singularities and without a good idea to solve the remaining integral, I arrived at: \begin{align*}...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.How did you obtain that?
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Does that simplify anything? I have the feeling we are left with the same old disgusting polynomials.
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I think it can be simplified in a better way by sorting the factor polynomials. But I agree, it doesn't look good. We have a circle...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.All correct, but it's almost impossible to integrate all that stuff. Take a look here. How about using the function ##\sinh^{-1}##...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I only needed ##z## as an intermediate variable. Expressing terms like ##p(y)/q'(y)## by ##z=q(y)## is almost impossible. So I...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
1) It was your integration that led to the minus sign. That also happens when we substitute the arctangent with a logarithm. I was...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Shouldn't we express this as a function of ##z##? How do we differentiate an expression in ##y## with respect to the variable ##z##?
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Mhm, there are some major problems. 1) Do we care that ##p(y)## is complex when ##y \in (-3,3)##? 2) When ##y=3##, ##z= i##. So we'd...
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
Here is my plan: \begin{align*} I&=2\int_{\sqrt{9-2\sqrt{8}}}^3 \left(p(y)\log\left|\sqrt{1+q(y)^2}+q(y)\right|\right) \,dy\\...
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MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Hope you'll be able to outline how to go on. For now I have no idea how to do it.
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MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I don't think that returning to ##\operatorname{arcsin}## would be an improvement. My formula is awkward if you ask me, even if it...