Question Number 210601 by mnjuly1970 last updated on 13/Aug/24 $$ \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:\:{the}\:\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }}…
Question Number 210593 by efronzo1 last updated on 13/Aug/24 $$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$ Answered by Sutrisno last updated on 30/Aug/24 $${misal} \\ $$$${cos}\mathrm{2}{x}={y}^{\mathrm{6}}…
Question Number 210517 by depressiveshrek last updated on 11/Aug/24 $$\int\frac{\mathrm{1}}{\mathrm{sin}{x}−\mathrm{cos2}{x}}{dx} \\ $$ Commented by Frix last updated on 11/Aug/24 $$\mathrm{Simply}\:\mathrm{use}\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\mathrm{to}\:\mathrm{get} \\ $$$$\frac{\mathrm{2}}{\mathrm{3}\left(\mathrm{1}+\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right)}+\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{9}}\mathrm{ln}\:\mid\frac{\mathrm{2}−\sqrt{\mathrm{3}}−\mathrm{tan}\:\frac{{x}}{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}−\mathrm{tan}\:\frac{{x}}{\mathrm{3}}}\mid\:+{C} \\ $$ Commented…
Question Number 210441 by universe last updated on 09/Aug/24 Answered by aleks041103 last updated on 09/Aug/24 $$\left({i}\right)\: \\ $$$${for}\:{odd}\:{n},\:{the}\:{function}\:{sin}^{{n}} \left({nx}\right)\:{is}\:{similar} \\ $$$${to}\:{sin}\left({x}\right)\:{with}\:{the}\:{fact}\:{that}\:{the}\:{primitive}\:{function}\:{oscilates} \\ $$$${between}\:\mathrm{0}\:{and}\:{the}\:{maximal}\:{possible}\:{value} \\…
Question Number 210396 by jirodomo last updated on 08/Aug/24 Commented by jirodomo last updated on 08/Aug/24 $$\mathrm{applying}\:\mathrm{partial}\:\mathrm{fraction}\:\mathrm{decomposition} \\ $$$$\mathrm{straight}\:\mathrm{away}\:\mathrm{seems}\:\mathrm{impossible}\:\mathrm{here}. \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{other}\:\mathrm{way}?\:\mathrm{im}\:\mathrm{stuck}\:\mathrm{for}\:\mathrm{a}\:\mathrm{few} \\ $$$$\mathrm{months}\:\mathrm{now}. \\ $$…
Question Number 210372 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$\mathrm{I}\:\mathrm{get}\:\pi^{\mathrm{2}} \\ $$ Answered by Berbere last updated on…
Question Number 210374 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$=\mathrm{Li}_{\mathrm{1000}} \:\left(\mathrm{1}\right) \\ $$$$\mathrm{Better}\:\mathrm{question}: \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{n}!}\underset{\mathrm{0}} {\overset{\infty}…
Question Number 210373 by Spillover last updated on 08/Aug/24 Commented by Frix last updated on 08/Aug/24 $$\mathrm{I}\:\mathrm{get}\:\mathrm{2ln}\:\mathrm{3} \\ $$ Commented by Spillover last updated on…
Question Number 210326 by Shrodinger last updated on 06/Aug/24 $$\int_{\mathrm{0}} ^{\pi} \:\frac{{tsin}\left({t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Commented by Spillover last updated on 06/Aug/24 $${i}\:{got}\:\mathrm{1}.\mathrm{6583}\:\:{is}\:{it}\:{right}? \\ $$…
Question Number 210095 by AlagaIbile last updated on 30/Jul/24 Commented by TonyCWX08 last updated on 01/Aug/24 $${Are}\:{you}\:{El}\:{Matematico}? \\ $$ Answered by Spillover last updated on…