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Category: Integration

Question-69597

Question Number 69597 by ozodbek last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${generally}\:{let}\:{find}\:{f}\left({a}\right)\:=\int\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${changement}\:{x}\:={ash}\left({t}\right)\:{give}\:{f}\left({a}\right)=\int{ach}\left({t}\right){ach}\left({t}\right){dt} \\ $$$$={a}^{\mathrm{2}}…

f-x-1-n-2-x-n-n-

Question Number 135103 by frc2crc last updated on 10/Mar/21 $${f}\left({x}\right)=\mathrm{1}+\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{{n}} \\ $$ Commented by Dwaipayan Shikari last updated on 10/Mar/21 $$\mathrm{1}−\left(−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}}…

let-f-a-0-dx-x-4-2x-2-a-with-a-real-and-a-gt-1-1-determine-a-explicit-form-for-f-a-2-calculate-g-a-0-dx-x-4-2x-2-a-2-3-find-the-values-of-integrals-0-

Question Number 69564 by mathmax by abdo last updated on 25/Sep/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+{a}}\:\:\:{with}\:{a}\:{real}\:{and}\:{a}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…