Question Number 104459 by bemath last updated on 21/Jul/20 $$\int\:\frac{{dx}}{\:\sqrt{{A}\mathrm{cos}\:{x}+{B}}} \\ $$ Commented by Dwaipayan Shikari last updated on 21/Jul/20 $$\int\frac{{dx}}{\:\sqrt{{Acosx}+{B}}}=\int\frac{{A}\left(−{sinx}\right)}{−{Asinx}}.\frac{\mathrm{1}}{\:\sqrt{{Acosx}+{B}}}{dx}\:\:\left\{{Acosx}+{B}={t}^{\mathrm{2}} \right. \\ $$$$\int\frac{\mathrm{2}{tdt}}{{t}\left(−{Asinx}\right)}=−\frac{\mathrm{2}}{{A}}\int\frac{\mathrm{1}}{{sinx}}{dt}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{cosx}=\left({t}^{\mathrm{2}} −{B}\right).\frac{\mathrm{1}}{{A}}\right.…
Question Number 38899 by math khazana by abdo last updated on 01/Jul/18 $${find}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}+{cost}\right){dt}\:{and}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}−{cost}\right){dt} \\ $$ Commented by maxmathsup by imad last…
Question Number 38896 by math khazana by abdo last updated on 01/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{x}\left[{x}\right]}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$ Commented…
Question Number 38897 by math khazana by abdo last updated on 01/Jul/18 $${find}\:\int\:{ln}\left(\sqrt{{x}}\:+\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}+\mathrm{2}}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104421 by mathmax by abdo last updated on 21/Jul/20 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{ch}\left(\mathrm{arctan}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 169930 by Mathspace last updated on 12/May/22 $${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104388 by Ar Brandon last updated on 21/Jul/20 $$\int\frac{\mathrm{d}{x}}{{x}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −\mathrm{1}}} \\ $$ Answered by Dwaipayan Shikari last updated on 21/Jul/20 $$\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}}…
Question Number 169906 by MikeH last updated on 12/May/22 $$\mathrm{Evaluate}\:\int\int{e}^{\mathrm{2}{x}+\mathrm{3}{y}} {dxdy}\:\mathrm{over}\:\mathrm{the}\:\mathrm{triangle} \\ $$$$\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{lines}\:{x}\:=\:\mathrm{0},\:{y}\:=\:\mathrm{0},\:{x}+{y}\:=\:\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104359 by bemath last updated on 21/Jul/20 $${solve}\:{this}\:{using}\:{Riemann} \\ $$$${sum}\:{f}\left({x}\right)=\mathrm{2}{x}\:;\:\left[\mathrm{0},\mathrm{4}\right]\:{for}\:{n}=\mathrm{4} \\ $$ Answered by Ar Brandon last updated on 21/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{4}} \mathrm{2}{x}\mathrm{d}{x}=\underset{\mathrm{n}\rightarrow\infty}…
Question Number 169873 by sciencestudent last updated on 11/May/22 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=? \\ $$ Answered by ArielVyny last updated on 11/May/22 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{{n}} {x}^{{n}} =\frac{\mathrm{1}}{\mathrm{1}+{x}}…