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Category: Integration

1-find-f-a-0-dx-x-4-a-with-a-gt-0-2-find-g-a-0-dx-x-4-a-2-3-find-value-of-integrals-0-dx-x-4-1-0-dx-2x-4-8-0-dx-x-4-1-2-an

Question Number 85160 by mathmax by abdo last updated on 19/Mar/20 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{a}}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{value}\:{of}\:{integrals}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}}…

calculate-U-n-1-n-1-n-x-2-1-x-1-x-dx-n-integr-and-n-2-2-find-nature-of-U-n-

Question Number 85158 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:{U}_{{n}} =\:\int_{−\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{1}}{{n}}} \:{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx}\:\:\:\left({n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Terms of Service Privacy Policy…

Question-150656

Question Number 150656 by mnjuly1970 last updated on 14/Aug/21 Answered by Ar Brandon last updated on 14/Aug/21 $$\Omega=\frac{\mathrm{1}}{\mathrm{2}}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\Gamma\left(\mathrm{1}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{2}}\right)\right) \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left(\sqrt{\pi}+\mathrm{1}+\frac{\sqrt{\pi}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{3}\sqrt{\pi}+\mathrm{2}\right) \\ $$ Commented by mnjuly1970…