A beautiful calculus problem 1

Somebody please provide the solution for this integral. Thanks a lot for the help. \(\int { [\ln { ({ e }^{ { x }^{ 2 } } } +1)\quad +\quad 2\{ \frac { { e }^{ { x }^{ 2 } }(2{ x }^{ 2 }-1)-1 }{ ({ e }^{ { x }^{ 2 } }+1)^{ 2 } } \} ]dx }\)

Note by Jay Verma
3 months, 2 weeks ago

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Can you explain what you have tried? What makes you think there is a beautiful solution to this problem?

Calvin Lin Staff - 3 months, 2 weeks ago

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Its not the solution but the problem that's beautiful.

Jay Verma - 3 months, 2 weeks ago

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What makes you think that there is a "nice" answer to this integral?

Or better yet, where did you find this integral?

Pi Han Goh - 3 months, 2 weeks ago

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Yeah, this link: http://durofy.com/5-most-beautiful-questions-from-integral-calculus/

Jay Verma - 3 months, 2 weeks ago

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What makes them "beautiful"? They all appear to be randomly constructed.

It's easy to see that Question 1 has a closed form via a simple substitution of y=x^pi + 7, but that doesn't make the integral beautiful.

Pi Han Goh - 3 months, 2 weeks ago

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@Pi Han Goh Care to say anything about the other 4 questions?

Jay Verma - 3 months, 2 weeks ago

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@Jay Verma They all appear to be randomly constructed.

Pi Han Goh - 3 months, 2 weeks ago

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@Pi Han Goh I don't find that reason good enough to undermine their beauty.

Jay Verma - 3 months, 2 weeks ago

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Someone please give a solution.

Jay Verma - 3 months, 2 weeks ago

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