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Category: Integration

0-arctan-1-x-2-

Question Number 134418 by mnjuly1970 last updated on 03/Mar/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \left({arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2}} =??? \\ $$ Answered by Ñï= last updated on 03/Mar/21 $$\int\left(\mathrm{tan}^{−\mathrm{1}}…

let-f-a-0-pi-2-dx-a-sinx-a-real-1-find-a-explicit-form-for-f-a-2-calculste-also-g-a-0-pi-2-dx-a-sinx-2-and-h-a-0-pi-2-dx-a-sinx-3-3-give-f-n-a-at

Question Number 68869 by mathmax by abdo last updated on 16/Sep/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{{a}+{sinx}}\:\:\:\:\:\left({a}\:{real}\right) \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculste}\:{also}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\left({a}+{sinx}\right)^{\mathrm{2}} }\:\:{and}\:{h}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\left({a}+{sinx}\right)^{\mathrm{3}} } \\…