Emmanuel José GarcíaI gave this integral as an answer at MathSE.
\[\int_{0}^{1}\left(\frac{5}{2} \left((x - \sqrt{x^2 - 1})^{2i} + x^4\right)-1\right)\,dx=e^\pi.\]
The integral yields \(e^{\pi}\). I don't know why the LaTeX isn't displaying properly.
#math #integral #eulernumber #halfangleapproach #symmetrymatters #calculus
Is there a definite integral that yields $e^\pi$ or $e^{-\pi}$ in a non trivial way?
The title says it all. No trivial answers like $\int_0^\pi e^tdt$ please. The idea is rather, if there are integrals like $$\int\limits_0^\infty \frac{t^{2n}}{\cosh t}dt=(-1)^{n}\left(\frac{\pi}2\r...
Kenneth
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