Question Number 39840 by math khazana by abdo last updated on 12/Jul/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\int_{{x}+\mathrm{1}} ^{{x}^{\mathrm{2}} \:+\mathrm{1}} \:\:{ln}\left(\mathrm{1}+{t}\right)\:{e}^{−{t}} {dt}\: \\ $$ Commented by abdo mathsup 649…
Question Number 39838 by math khazana by abdo last updated on 12/Jul/18 $${find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}\: \\ $$ Commented by maxmathsup by imad…
Question Number 39836 by math khazana by abdo last updated on 12/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \frac{{ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right)}{\mathrm{2}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 39833 by math khazana by abdo last updated on 12/Jul/18 $${find}\:\:\int\:\:\:\:\frac{{ln}\left({x}+\sqrt{{x}^{\mathrm{2}} \:−\mathrm{1}}\right)}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\frac{{ln}\left({x}+\sqrt{{x}^{\mathrm{2}} \:−\mathrm{1}}\right.}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$ Commented by…
Question Number 39834 by math khazana by abdo last updated on 12/Jul/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:\mid\:{cos}\left(\mathrm{2}{x}\right)−{cos}\left(\mathrm{3}{x}\right)\mid{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 12/Jul/18 $$\int_{\mathrm{0}}…
Question Number 105353 by abdomsup last updated on 28/Jul/20 $${solve}\:{y}^{''\:} +\mathrm{2}{y}^{'} −{y}\:={x}^{{n}} \:{e}^{−{x}} \\ $$$${n}\:{integr}\:{natural} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 170871 by sciencestudent last updated on 02/Jun/22 $${Why}\:{is}\:{it}\:{equal}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{0}} {\overset{\pi} {\int}}{sin}^{\mathrm{2}{p}} {udu}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{sin}^{\mathrm{2}{p}} {udu} \\ $$ Answered by thfchristopher last updated…
Question Number 39787 by abdo mathsup 649 cc last updated on 10/Jul/18 $${calculste}\:\:{I}_{\lambda} \:=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\lambda{x}^{{n}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with} \\ $$$$\lambda\:{from}\:{R}\:{and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{vslue}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\mathrm{3}\:{x}^{\mathrm{9}} \right)}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 170855 by mnjuly1970 last updated on 01/Jun/22 $$ \\ $$$$\:\:\:\lfloor{x}\rfloor=\:{log}_{\mathrm{2}} \left(\mathrm{4}^{\:{x}} −\mathrm{2}^{\:{x}} −\mathrm{1}\right)\Rightarrow\:\lfloor\:\mathrm{4}^{\:{x}} \rfloor=? \\ $$$$ \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 170831 by venom1 last updated on 01/Jun/22 Answered by LEKOUMA last updated on 01/Jun/22 $$\left.\mathrm{1}\right)\:\int\mathrm{4sin}\:\mathrm{8}{xdx}=\mathrm{4}\int\mathrm{sin}\:\mathrm{8}{xdx}=\mathrm{4}×−\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{8}{x}+{c}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{8}{x}+{c} \\ $$$$\left.\mathrm{2}\right)\:\int{x}\mathrm{cos}\:\left(\mathrm{12}{x}^{\mathrm{2}} \right){dx} \\ $$$${let}\:{u}=\mathrm{12}{x}^{\mathrm{2}} \:\Rightarrow\:{du}=\mathrm{24}{xdx}\:\Rightarrow\:{dx}=\frac{{du}}{\mathrm{24}{x}} \\ $$$$\int\frac{\mathrm{1}}{\mathrm{24}}\mathrm{cos}\left(\:{u}\right){du}=\frac{\mathrm{1}}{\mathrm{24}}\int\mathrm{cos}\:\left({u}\right){du}=\frac{\mathrm{1}}{\mathrm{24}}\mathrm{sin}\left(\:{u}\right)+{c}…