Question Number 101940 by Dwaipayan Shikari last updated on 05/Jul/20 $$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left({ne}^{\frac{−\mathrm{1}}{{n}^{\mathrm{2}} }} +{ne}^{\frac{−\mathrm{4}}{{n}^{\mathrm{2}} }} +…..\infty\right) \\ $$ Answered by Ar Brandon last updated…
Question Number 36406 by abdo mathsup 649 cc last updated on 01/Jun/18 $${find}\:{the}\:{values}\:{of}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\pi} {cos}^{\mathrm{4}} {dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\pi} \:{sin}^{\mathrm{4}} {dx}\:. \\ $$ Commented by…
Question Number 36394 by abdo.msup.com last updated on 01/Jun/18 $${let}\:{f}\left({x}\right)={artanx}\:{find}\:\:{L}\left({f}\left({x}\right)\right) \\ $$$${L}\:{mean}\:{laplace}\:{trsnsform}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 36397 by prof Abdo imad last updated on 01/Jun/18 $${find}\:{I}\:\:=\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\:\:\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\:\:+\left({x}+\mathrm{1}\right)\sqrt{{x}}} \\ $$$$ \\ $$ Answered by behi83417@gmail.com last updated on 01/Jun/18…
Question Number 36393 by abdo.msup.com last updated on 01/Jun/18 $${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}}{{sinx}}\:\:\:,\mathrm{2}\pi\:{periodic}\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167438 by cortano1 last updated on 16/Mar/22 $$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{4sin}\:^{\mathrm{4}} \mathrm{x}−\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}=? \\ $$ Answered by MJS_new last updated on 16/Mar/22 $$\frac{\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}\:+\mathrm{4sin}^{\mathrm{4}} \:{x}}=\frac{\mathrm{2sin}\:\mathrm{4}{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{4}{x}}=\frac{\mathrm{2sin}\:\mathrm{2}{x}\:\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}}=…
Question Number 167433 by mnjuly1970 last updated on 16/Mar/22 $$ \\ $$$$\:\:\:\:\:\:\:{calculate}\: \\ $$$$\:\:\:\:\mathrm{1}\::\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\:{H}_{\:{n}} }{{n}}\:\right)^{\:\mathrm{2}} =\:? \\ $$$$\:\:\:\:\mathrm{2}\::\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}^{\:\mathrm{2}} \left({x}\right).\mathrm{L}{i}_{\:\mathrm{2}} \left({x}\right)}{{x}}\:{dx}\:=\:? \\…
Question Number 167416 by Coronavirus last updated on 16/Mar/22 $$\int_{\:\mathrm{0}} ^{\:\pi} \:\frac{{x}.\mathrm{sin}\:\left({x}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\:\pi} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}^{\mathrm{3}} \left({x}\right)\:+\mathrm{sin}^{\mathrm{3}} \left({x}\right)\:}{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}}…
Question Number 36335 by prof Abdo imad last updated on 31/May/18 $${find}\:\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{arctan}\left({tx}^{\mathrm{2}} \right){dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${developp}\:\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by prof Abdo imad last…
Question Number 36336 by prof Abdo imad last updated on 31/May/18 $${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{arctan}\left({xt}^{\mathrm{2}} \right){dt}\:{with}\:{x}>\mathrm{0} \\ $$ Commented by abdo.msup.com last updated on 01/Jun/18 $${we}\:{have}\:{f}^{'}…