Category: Integration

Question Number 104505 by mathmax by abdo last updated on 22/Jul/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$ Answered by OlafThorendsen last updated on…

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 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 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 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}}…