Question Number 117979 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mid\:\:\Gamma\:\left(\:{i}\:\right)\:\mid\overset{?} {=}\:\sqrt{\frac{\pi}{{sinh}\left(\pi\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\Gamma:\:\mathscr{E}{uler}\:{gamma}\:{function}\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Commented by…
Question Number 117963 by peter frank last updated on 14/Oct/20 Answered by john santu last updated on 14/Oct/20 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \left({x}^{\mathrm{3}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} \:}\:\right){dx}\:=\:\mathrm{0} \\ $$$${then}\:\int_{−\mathrm{2}}…
Question Number 52418 by Abdo msup. last updated on 07/Jan/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 08/Jan/19…
Question Number 117948 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{integral}…\: \\ $$$$\:\:\:{please}\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({sin}\left({x}\right)+{sin}\left(\frac{\mathrm{1}}{{x}}\right)\right)\frac{{dx}}{{x}}\:=?? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\:\: \\…
Question Number 117944 by bemath last updated on 14/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{satisfies}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\left(\frac{\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{x}}}{\:\sqrt{\mathrm{2k}}}\:\right)\:\mathrm{dx}\:=\:\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$ \\ $$ Answered by john santu last updated on…
Question Number 117945 by bemath last updated on 14/Oct/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\int\:\frac{\mathrm{5x}^{\mathrm{8}} +\mathrm{7x}^{\mathrm{6}} }{\left(\mathrm{2x}^{\mathrm{7}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}\:\mathrm{and}\:\: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:,\:\mathrm{then}\:\mathrm{f}\left(\mathrm{1}\right)\:=\:\_\: \\ $$ Commented by bemath last updated on…
Question Number 183450 by cortano1 last updated on 26/Dec/22 $$\:\underset{\mathrm{0}} {\overset{{x}^{\mathrm{2}} } {\int}}\:{f}\left(\mathrm{2}{t}^{\mathrm{3}} −{t}^{\mathrm{2}} −\mathrm{6}\right){dt}\:=\:\mathrm{ln}\:{x}\: \\ $$$$\:{then}\:{f}\left(\mathrm{106}\right)=? \\ $$ Answered by mahdipoor last updated on…
Question Number 117910 by bemath last updated on 14/Oct/20 $$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$ Commented by bemath last updated on 14/Oct/20 Answered by Lordose last updated…
Question Number 52363 by Necxx last updated on 06/Jan/19 $${integrate}\:\frac{\mathrm{sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}\:}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jan/19 $$=\left(−\mathrm{1}\right)\int\frac{\mathrm{1}−{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}}…
Question Number 52356 by Tawa1 last updated on 06/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jan/19 Commented by Tawa1 last updated on 07/Jan/19 $$\mathrm{Sir}\:\mathrm{please}\:\mathrm{help}. \\…