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Author: Tinku Tara

let-f-x-0-1-dt-ch-t-xsh-t-1-find-a-explicit-form-of-f-x-2-determine-g-x-0-1-dt-ch-t-xsh-t-2-3-calculate-0-1-dt-ch-t-3sh-t-and-0-1-dt-ch-t-3sh-t-

Question Number 66062 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+{xsh}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left({ch}\left({t}\right)+{xsh}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+\mathrm{3}{sh}\left({t}\right)}\:{and}\:\int_{\mathrm{0}}…

let-f-x-0-pi-4-dt-x-tant-with-x-real-1-find-aexplicit-form-of-f-x-2-find-also-g-x-0-pi-4-dt-x-tant-2-3-give-f-n-x-at-form-of-integral-4-calculate-0-pi-4-dt-2

Question Number 66060 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{{x}+{tant}}\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{aexplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{\left({x}+{tant}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({x}\right){at}\:{form}\:{of}\:{integral} \\…