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HSC 2018-2019 MX2 Integration Marathon (1 Viewer)

Paradoxica

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I don't believe it has a solution contained within MX2. But feel free to take that as a challenge.
 

fan96

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I'm really lost. I tried to express the integral in various alternative ways but I can't solve any of these.:mad:





Have you tried writing the last one in terms of the hyperbolic functions?
 

sharky564

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I'm really lost. I tried to express the integral in various alternative ways but I can't solve any of these.:mad:





That's an excellent variety of integrals, none of which are on the right track (from what I've explored at least). My method is not that nice but it does yield a solution. My first hint is to try in the original integral.
 

stupid_girl

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Many alternative forms that lead me to nowhereo_O
Why is pi^2/8 appearing so often?






 

sharky564

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Many alternative forms that lead me to nowhereo_O
Why is pi^2/8 appearing so often?






That's what I like about this question - due to the simplicity of the q, there seem to be so many ways of approaching it which don't go anywhere
 

sharky564

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Another problem if u get bored of that one:



No using dilogarithms, only 4U stuff.
 

sharky564

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Do you have more hints?
After a partial evaluation of the integral, you should get the original integral, which you can use for symmetry. See how that's possible. (note that this is quite cancerous to do, so you need to have some persistence)
 

stupid_girl

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A few more alternative expressions that look interesting but not leading to a solution:frown2:




 

stupid_girl

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I have decided to give up @sharky564 question.

This is a new question that should be solvable in 4U.
 
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stupid_girl

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One more question

(It can be solved without knowing the result in #217.🤓)
 

stupid_girl

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This question can take ages if you're not on the right track.:mad:

(modified to make it look more evil😈...feel free to share your attempt)
 
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HeroWise

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why does Sharkys Integral look much easier compared to that
 

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