Question Number 123703 by Algoritm last updated on 27/Nov/20 Answered by MJS_new last updated on 27/Nov/20 $$=\int\left(\mathrm{cos}\:{x}\right)^{\mathrm{5}/\mathrm{3}} {dx} \\ $$$$\mathrm{use}\:\mathrm{these}\:\mathrm{formulas}: \\ $$$$\int\left(\mathrm{sin}\:{x}\right)^{{p}/{q}} {dx}=\frac{{q}}{{p}+{q}}\left(\mathrm{sin}\:{x}\right)^{\frac{{p}+{q}}{{q}}} \:_{\mathrm{2}} \mathrm{F}_{\mathrm{1}}…
Question Number 58168 by maxmathsup by imad last updated on 19/Apr/19 $${find}\:\int\:\:\:\:\frac{\sqrt{{tanx}}}{{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Answered by tanmay last updated on 19/Apr/19 $$\int\frac{\sqrt{{tanx}}\:}{\mathrm{2}{tanx}}×\left(\mathrm{1}+{tan}^{\mathrm{2}} {x}\right){dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{sec}^{\mathrm{2}}…
Question Number 123687 by mnjuly1970 last updated on 27/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}.. \\ $$$$\:{prove}\:{that}::\:\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{2}\phi\left({x}\right)}{{x}^{\mathrm{2}} }\:+\frac{\pi^{\mathrm{2}} }{\mathrm{3}{x}}\right)\:\overset{???} {=}\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:{where} \\ $$$$\:\:\:\:\:\phi\left({x}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left({t}^{{x}} −\mathrm{1}\right)\left({ln}\left(\mathrm{1}−{t}\right)\right)}{{tln}\left({t}\right)}{dt} \\ $$…
Question Number 123676 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{2x}} \right)\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 27/Nov/20…
Question Number 123674 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 123673 by mathmax by abdo last updated on 27/Nov/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\right)^{\mathrm{4}} \mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 189189 by MikeH last updated on 13/Mar/23 Answered by cortano12 last updated on 13/Mar/23 $$\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}+\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx} \\ $$$$=\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}}…
Question Number 123639 by benjo_mathlover last updated on 26/Nov/20 $$\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\sqrt{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}\:{dx}\:? \\ $$ Answered by MJS_new last updated on 27/Nov/20 $${x}\rightarrow+\infty\:\Rightarrow\:\mathrm{arctan}\:{x}\:\rightarrow\:\frac{\pi}{\mathrm{2}}\:\Rightarrow \\ $$$$\mathrm{integral}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{converge}…
Question Number 189144 by talminator2856792 last updated on 12/Mar/23 $$\: \\ $$$$\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\sqrt{{x}\:+\:{y}\:+\:{z}}}{\:\sqrt{{x}}\:+\:\sqrt{{y}}\:+\:\sqrt{{z}}\:}\:{dxdydz} \\ $$$$\: \\ $$$$\: \\…
Question Number 123552 by Lordose last updated on 26/Nov/20 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Adeleke last updated on 26/Nov/20 Answered by TANMAY…