Question Number 6699 by jose14918645@gmail.com last updated on 14/Jul/16 $$\int\left({e}^{{x}} +\mathrm{1}\right){e}^{{x}} {dx} \\ $$ Answered by FilupSmith last updated on 14/Jul/16 $$=\int{e}^{\mathrm{2}{x}} +{e}^{{x}} {dx} \\…
Question Number 6700 by jose14918645@gmail.com last updated on 14/Jul/16 $$\int\left({e}^{−\mathrm{2}+\mathrm{2}} {xdx}\right. \\ $$ Answered by FilupSmith last updated on 15/Jul/16 $$=\int{e}^{\mathrm{0}} {xdx} \\ $$$$=\int{xdx} \\…
Question Number 137770 by peter frank last updated on 06/Apr/21 Answered by Ñï= last updated on 06/Apr/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} {da}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}}{\left(\mathrm{1}+{ax}\right)\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 6686 by FilupSmith last updated on 13/Jul/16 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {e}^{−{ix}^{\mathrm{2}} } {dx}=\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{{i}}{\mathrm{2}}\right)\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$ Commented by FilupSmith last updated on 14/Jul/16…
Question Number 6665 by Yozzii last updated on 10/Jul/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} {sinh}^{\mathrm{1}/{n}} {x}\:{dx}=?\:,\:{n}\in\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137717 by mnjuly1970 last updated on 05/Apr/21 Commented by Dwaipayan Shikari last updated on 05/Apr/21 $${f}\left({a}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Gamma\left(\frac{{a}+\mathrm{1}}{\mathrm{2}}\right)\Gamma\left(\frac{\mathrm{3}−{a}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}−{a}}{\mathrm{2}}\right)\Gamma\left(\frac{{a}+\mathrm{1}}{\mathrm{2}}\right)\Gamma\left(\frac{\mathrm{1}−{a}}{\mathrm{2}}\right)=\frac{\mathrm{1}−{a}}{\mathrm{4}}.\frac{\pi}{{sin}\left(\frac{\pi}{\mathrm{2}}+\frac{\pi}{\mathrm{2}}{a}\right)} \\ $$$$=\frac{\pi}{\mathrm{4}}\left(\mathrm{1}−{a}\right){sec}\left(\frac{\pi}{\mathrm{2}}{a}\right) \\ $$$$−\frac{\mathrm{1}}{\mathrm{3}}{f}'\left(\mathrm{0}\right)=\frac{\pi}{\mathrm{12}} \\ $$ Terms…
Question Number 137697 by Mathspace last updated on 05/Apr/21 $${let}\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1} \\ $$$${find}\:\:\int\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:{and}\:\int\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx} \\ $$ Commented by TheSupreme last updated on 07/Apr/21 $${f}^{−\mathrm{1}}…
Question Number 137696 by Mathspace last updated on 05/Apr/21 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({nsinx}\right)−{sin}\left({ncosx}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$${determine}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} {e}^{−{n}^{\mathrm{2}} } \:{U}_{{n}} \\ $$…
Question Number 137695 by Mathspace last updated on 05/Apr/21 $${find}\:\:\int\:\:\frac{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{3}} }{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}}{dx} \\ $$ Answered by bemath last updated on 05/Apr/21 $$\:\int\:\frac{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\sqrt{{x}}−\sqrt{{x}+\mathrm{1}}\:\right)}{{x}−\left({x}+\mathrm{1}\right)}{dx} \\ $$$$=\:\int\:\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}}\:\right){dx}…
Question Number 137693 by Mathspace last updated on 05/Apr/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({sinx}\right)−{sin}\left({cosx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx} \\ $$ Answered by mathmax by abdo last updated on 07/Apr/21 $$\int_{\mathrm{0}}…