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Category: Integration

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}} } \\…

0-x-2-1-x-2-4-dx-

Question Number 134301 by bramlexs22 last updated on 02/Mar/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{4}} }\:{dx} \\ $$ Answered by EDWIN88 last updated on 02/Mar/21 $$\mathrm{replace}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{yields}\:…

F-0-16-arctan-x-1-x-2-dx-

Question Number 134303 by bramlexs22 last updated on 02/Mar/21 $$\mathcal{F}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{16}\:\mathrm{arctan}\:\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Answered by Ñï= last updated on 02/Mar/21 $$\mathcal{F}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{16}\:\mathrm{arctan}\:\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}}…