Question Number 197177 by Mathspace last updated on 09/Sep/23 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cosx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197111 by cortano12 last updated on 08/Sep/23 $$\:\:\:\:\:\:\cancel{ } \\ $$ Answered by Frix last updated on 08/Sep/23 $$\int\frac{{dx}}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} \:{x}\:\mathrm{sin}^{\mathrm{5}} \:{x}}}\:\overset{{t}=\mathrm{tan}\:{x}} {=} \\…
Question Number 197060 by universe last updated on 07/Sep/23 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$ Commented by universe last updated on 07/Sep/23 $${question}\:\mathrm{196950}…
Question Number 197024 by mnjuly1970 last updated on 06/Sep/23 $$ \\ $$$$\:\:\:\:\:\:{calculate} \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}\left({x}\right)\:\sqrt{\:\mathrm{1}\overset{} {+}\:{sin}\left({x}\right){cos}\left({x}\right)}\:{dx}=? \\ $$$$ \\ $$ Answered by Frix last…
Question Number 196983 by universe last updated on 05/Sep/23 Commented by Frix last updated on 06/Sep/23 $$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{first}\:\mathrm{2}\:\mathrm{but}\:\mathrm{wolframalpha}\:\mathrm{can} \\ $$$$\left(\mathrm{C}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Catalan}\:\mathrm{constant}\right) \\ $$$$\mathrm{1}.\:{I}_{\mathrm{1}} =\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}^{\mathrm{3}} }{…}{dx}=\frac{\pi\left(−\mathrm{1440C}+\mathrm{1144}+\mathrm{15}\pi\left(−\mathrm{41}+\mathrm{20}\pi+\mathrm{24ln}\:\mathrm{2}\right)\right)}{\mathrm{3780}}…
Question Number 196832 by Frix last updated on 01/Sep/23 $$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$ Commented by mokys last updated on 02/Sep/23 $${u}\:=\:\frac{\mathrm{1}}{\mathrm{2}{x}}\:\rightarrow\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}{u}}\:\rightarrow\:{dx}\:=\:−\:\frac{{du}}{\mathrm{2}{u}^{\mathrm{2}} } \\ $$$$ \\…
Question Number 196817 by universe last updated on 01/Sep/23 Answered by witcher3 last updated on 04/Sep/23 $$\mathrm{are}\:\mathrm{You}\:\mathrm{sur}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}? \\ $$ Commented by universe last updated on…
Question Number 196788 by ERLY last updated on 31/Aug/23 $${calculer}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$<{erly}\:{rolvinst}> \\ $$$$ \\ $$ Answered by MrGHK last updated on…
Question Number 196688 by cortano12 last updated on 29/Aug/23 Answered by Frix last updated on 29/Aug/23 $$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:{dx}\:\overset{{t}=\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}} {=} \\ $$$$=\int\frac{{t}^{\mathrm{4}} −\mathrm{4}}{{t}^{\mathrm{2}} }{dt}=\frac{{t}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{4}}{{t}}=…
Question Number 196557 by BHOOPENDRA last updated on 27/Aug/23 Answered by qaz last updated on 27/Aug/23 $$\int_{\mathrm{0}} ^{{t}} {e}^{−{u}} \mathrm{sin}\:{udu}=−\Im\int_{\mathrm{0}} ^{{t}} {e}^{−\left(\mathrm{1}+{i}\right){u}} {du}=\Im\frac{\mathrm{1}}{\mathrm{1}+{i}}\left({e}^{−\left(\mathrm{1}+{i}\right){t}} −\mathrm{1}\right) \\…