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Category: Integration

find-arctan-1-x-1-dx-

Question Number 67017 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{I}\:=\int\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx}\:\:{changement}\:\sqrt{{x}+\mathrm{1}}={t}\:{give}\:{x}+\mathrm{1}={t}^{\mathrm{2}} \:\Rightarrow…

let-f-x-0-dt-x-2-t-2-2-with-x-gt-0-1-find-a-explicit-form-of-x-2-find-also-g-x-0-dt-x-2-t-2-3-3-find-the-values-of-integrals-0-dt-t-2-3-2-

Question Number 67008 by mathmax by abdo last updated on 21/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}}…