Question Number 31107 by abdo imad last updated on 02/Mar/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }\:\:{with}\:{n}>\mathrm{1}. \\ $$ Commented by abdo imad last updated on 06/Mar/18…
Question Number 162177 by mnjuly1970 last updated on 27/Dec/21 $$ \\ $$$$\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{ln}^{\:\mathrm{2}} \left(\:{x}\:\right).\:\mathrm{Li}_{\:\mathrm{2}} \:\left({x}\:\right)}{{x}^{\:} }\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated…
Question Number 31105 by abdo imad last updated on 02/Mar/18 $${prove}\:{that}\:\int_{\mathrm{0}} ^{{x}} \:\:\:{e}^{−{t}^{\mathrm{2}} } {dt}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:−\frac{{e}^{−{x}^{\mathrm{2}} } }{\:\sqrt{\pi}}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{x}^{\mathrm{2}} {t}^{\mathrm{2}} } }{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:{with}\:{x}>\mathrm{0} \\ $$…
Question Number 31106 by abdo imad last updated on 02/Mar/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}^{\mathrm{2}} } ={lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:. \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\frac{\mathrm{1}}{\:\sqrt{\pi}}\:={lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}….\left(\mathrm{2}{n}−\mathrm{3}\right)}{\mathrm{2}.\mathrm{4}.\mathrm{6}….\left(\mathrm{2}{n}−\mathrm{2}\right)}\:\sqrt{{n}} \\ $$$$\left({wallis}\:{formula}\right).…
Question Number 31102 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{lnx}}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnx}}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{3}} }\:. \\ $$ Commented…
Question Number 31103 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}\:−\frac{{a}}{{x}}\right)^{\mathrm{2}} } {dx}\:\:{with}\:\:{a}\geqslant\mathrm{0}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31104 by abdo imad last updated on 02/Mar/18 $${find}\:\:\:\:\int_{−\infty} ^{+\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{1}\right)} {dx}\:. \\ $$ Commented by abdo imad last updated on 03/Mar/18…
Question Number 31101 by abdo imad last updated on 02/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:{t}^{\mathrm{2}} \:{e}^{−\mathrm{2}{t}^{\mathrm{2}} } {sin}\left(\mathrm{2}\left({x}−{t}\right)\right){dt}\:{calculate} \\ $$$${f}^{''} \:+\mathrm{4}{f}\:\:{then}\:{finf}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy…
Question Number 96637 by 175 last updated on 03/Jun/20 Commented by bemath last updated on 03/Jun/20 $$\int\:\frac{\mathrm{ln}\left(\mathrm{x}^{\mathrm{a}} \right)}{\mathrm{x}}\:\mathrm{dx}\:=\:\mathrm{a}\int\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{let}\:\mathrm{u}\:=\:\mathrm{ln}\:\left(\mathrm{x}\right)\:\Rightarrow\:\mathrm{du}\:=\:\frac{\mathrm{dx}}{\mathrm{x}} \\ $$$$\Rightarrow\mathrm{a}\int\:\mathrm{u}\:\mathrm{du}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\:\mathrm{u}^{\mathrm{2}} +\mathrm{c}\: \\ $$$$=\:\frac{\mathrm{a}}{\mathrm{2}}\:\left(\mathrm{ln}\left(\mathrm{x}\right)\right)^{\mathrm{2}}…
Question Number 162174 by mnjuly1970 last updated on 27/Dec/21 $$ \\ $$$$\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{4}{x}\:−\mathrm{1}=\mathrm{0}\:\: \\ $$$$\:\:\:\:\:\alpha\:,\:\beta\:\:{are}\:{roots}\: \\ $$$$\:\:\:\:\:\alpha^{\:\mathrm{3}} \:+\:\mathrm{17}\beta\:+\mathrm{5}\:=? \\ $$$$\:\:−−−{solution}−−− \\ $$$$\:\:\:\alpha\:\:\:{is}\:{root}\:\:\:\Rightarrow\:\alpha^{\:\mathrm{2}} −\mathrm{4}\alpha\:−\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\Rightarrow\:\alpha^{\:\mathrm{2}}…