Question Number 186771 by mnjuly1970 last updated on 10/Feb/23 $$ \\ $$$$\:\:\:\:\mathrm{Q}\::\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral}.\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\frac{\:\pi}{\:\mathrm{2}}} \:\frac{\:\:\mathrm{1}}{\:\mathrm{1}\:+\:\mathrm{sin}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:+\:\mathrm{cos}^{\:\mathrm{4}} \:\left(\:{x}\:\right)\:}\:\mathrm{d}{x}\:=\:\:?\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…
Question Number 121224 by liberty last updated on 06/Nov/20 $$\:\:\:\:\int\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{dx}\: \\ $$ Answered by benjo_mathlover last updated on 06/Nov/20 $$\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=\:−\int\:\frac{\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)\:\mathrm{d}\left(\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}} \\…
Question Number 121225 by benjo_mathlover last updated on 06/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{5}} \:\sqrt{\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 06/Nov/20 $$\:\mathrm{let}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 55672 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{\mid{z}\mid=\mathrm{1}} \left({z}^{\mathrm{2}} \mathrm{sin}\:\frac{\mathrm{1}}{{z}}+\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\mathrm{sin}\:{z}\right)\:{dz}\:\mathrm{is}… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 55668 by mr W last updated on 01/Mar/19 $${Find}\:{all}\:{functions}\:{y}={f}\left({x}\right)\:{such}\:{that} \\ $$$${y}'{y}''={y}'''. \\ $$ Commented by malwaan last updated on 02/Mar/19 $$\mathrm{y}=\mathrm{e}^{\mathrm{x}} \\ $$…
Question Number 186736 by Rupesh123 last updated on 09/Feb/23 Answered by Frix last updated on 09/Feb/23 $$\lfloor\frac{\mathrm{2}^{\mathrm{0}} }{\mathrm{3}}\rfloor=\mathrm{0}\:\Rightarrow \\ $$$${A}_{\mathrm{2}{n}} =\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\lfloor\frac{\mathrm{2}^{{i}} }{\mathrm{3}}\rfloor=\underset{{i}=\mathrm{1}} {\overset{{n}}…
Question Number 121203 by benjo_mathlover last updated on 05/Nov/20 $$\:\int\:\frac{\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{sin}\:\left(\mathrm{x}\right)}}\:\mathrm{dx}\: \\ $$ Answered by MJS_new last updated on 06/Nov/20 $$\int\frac{\mathrm{cos}^{\mathrm{5}} \:{x}}{\:\sqrt{\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{sin}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{2}\sqrt{\mathrm{sin}\:{x}}}{\mathrm{cos}\:{x}}{dt}\right] \\…
Question Number 186735 by Rupesh123 last updated on 09/Feb/23 Answered by Ar Brandon last updated on 09/Feb/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{ln}\left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2023}} {dx}\:,\:{t}=−\mathrm{ln}{x}\:\Rightarrow{x}={e}^{−{t}} \\ $$$$\:\:=\int_{\mathrm{0}} ^{\infty} {t}^{\mathrm{2023}}…
Question Number 186726 by Rupesh123 last updated on 09/Feb/23 Answered by cortano12 last updated on 09/Feb/23 $${f}\:'\left({x}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{ln}\:{x}^{\mathrm{3}} }=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{ln}\:{ex}^{\mathrm{3}} } \\ $$$${f}\:''\left({x}\right)=\:\frac{\mathrm{6}{x}.\mathrm{ln}\:{ex}^{\mathrm{3}} −\frac{\mathrm{3}{ex}^{\mathrm{2}} }{{ex}^{\mathrm{3}}…
Question Number 121174 by benjo_mathlover last updated on 05/Nov/20 $$\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{ln}\:\left(\frac{\pi+\mathrm{x}}{\pi−\mathrm{x}}\right)\right)\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:? \\ $$ Answered by TANMAY PANACEA last updated on 05/Nov/20 $${I}=\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}}…