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Category: Integration

e-2x-2-x-dx-

Question Number 106391 by Ar Brandon last updated on 05/Aug/20 $$\int\mathrm{e}^{\mathrm{2x}^{\mathrm{2}} +\mathrm{x}} \mathrm{dx} \\ $$ Answered by Sarah85 last updated on 05/Aug/20 $${t}=\sqrt{\mathrm{2}}\left({x}+\frac{\mathrm{1}}{\mathrm{4}}\right)\:\Leftrightarrow\:{x}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{t}−\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\:{dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{dt} \\ $$$$\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\mathrm{e}^{{t}^{\mathrm{2}}…

dx-9-4x-2-using-the-trigonometric-substitution-

Question Number 171910 by Tawa11 last updated on 21/Jun/22 $$\int\:\frac{\mathrm{dx}}{\mathrm{9}\:\:\:−\:\:\:\mathrm{4x}^{\mathrm{2}} } \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{substitution}. \\ $$ Answered by aleks041103 last updated on 21/Jun/22 $$\int\frac{{dx}}{\mathrm{9}−\mathrm{4}{x}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{9}}\int\frac{{dx}}{\mathrm{1}−\left(\frac{\mathrm{2}{x}}{\mathrm{3}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{9}}\:\frac{\mathrm{3}}{\mathrm{2}}\int\frac{{du}}{\mathrm{1}−{u}^{\mathrm{2}}…

let-f-t-0-arctan-tx-x-3-8-dx-1-find-a-simple-form-of-f-t-2-calculate-0-arctan-x-x-3-8-dx-

Question Number 40829 by math khazana by abdo last updated on 28/Jul/18 $${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({tx}\right)}{{x}^{\mathrm{3}} +\mathrm{8}}{dx} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}\right)}{{x}^{\mathrm{3}} \:+\mathrm{8}}{dx}\:. \\ $$…

help-n-1-1-2n-1-

Question Number 106365 by Mikael_786 last updated on 04/Aug/20 $$\mathrm{help} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)!} \\ $$ Commented by Dwaipayan Shikari last updated on 04/Aug/20 $${or}\:{sin}\:{h}\left(\mathrm{1}\right)…