Question Number 223090 by MrGaster last updated on 14/Jul/25
$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{cosh}\left({x}^{\mathrm{2}} \right)\right)^{\mathrm{2}} }\mathrm{d}{x} \\ $$
Commented by Tawa11 last updated on 18/Jul/25
$$\mathrm{I}\:\mathrm{got}:\:\:\:\:\:\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{\mathrm{2}}}\:\eta\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:\:\:\mathrm{where}\:\:\eta\:\:\mathrm{is}\:\:'\mathrm{Eta}'\:\:\mathrm{function}. \\ $$$$\mathrm{Or} \\ $$$$\:\:\:\:\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{\mathrm{2}}}\:\left(\mathrm{1}\:\:−\:\:\sqrt{\mathrm{2}}\right)\zeta\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$
Answered by zetamaths last updated on 14/Jul/25
$${is}\:{not}\:{possible}.\theta\:{and}\:{d}\theta \\ $$