Question Number 189949 by Universmathematiques last updated on 24/Mar/23 Answered by witcher3 last updated on 25/Mar/23 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\sqrt[{\mathrm{2}}]{\mathrm{x}\sqrt[{\mathrm{3}}]{\mathrm{x}\sqrt[{\mathrm{4}}]{}}…} \\ $$$$\mathrm{ln}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{ln}\left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{6}}\mathrm{ln}\left(\mathrm{x}\right)….. \\ $$$$\mathrm{ln}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{k}!}=\mathrm{ln}\left(\underset{\mathrm{k}\geqslant\mathrm{1}} {\prod}\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{k}!}} \right)=\mathrm{ln}\left(\mathrm{x}^{\underset{\mathrm{m}\geqslant\mathrm{1}}…
Question Number 124371 by bemath last updated on 02/Dec/20 $$\:\int\:\frac{{e}^{{x}} \left(\mathrm{2}−\mathrm{sin}\:\mathrm{2}{x}\right)}{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}}\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on 02/Dec/20 $$\int{e}^{{x}} \left(\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}−\frac{{cosx}}{{sinx}}\right){dx} \\…
Question Number 124360 by Lordose last updated on 02/Dec/20 $$\int_{\:\mathrm{0}} ^{\:\infty} \frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 02/Dec/20…
Question Number 124352 by Mammadli last updated on 02/Dec/20 $$\underset{\mathrm{0}} {\overset{\mathrm{4}\pi} {\int}}\parallel{cosx}\parallel=? \\ $$ Commented by mr W last updated on 02/Dec/20 $${do}\:{you}\:{mean}\:\underset{\mathrm{0}} {\overset{\mathrm{4}\pi} {\int}}\mid{cosx}\mid\:{dx}\:?…
Question Number 189890 by mnjuly1970 last updated on 23/Mar/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124334 by Ar Brandon last updated on 02/Dec/20 $$\int\sqrt{\frac{\mathrm{cos}{x}−\mathrm{cos}^{\mathrm{3}} {x}}{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{3}} {x}\right)}}\mathrm{d}{x} \\ $$ Answered by MJS_new last updated on 02/Dec/20 $$=\int\frac{\mathrm{sin}\:{x}\:\sqrt{\mathrm{cos}\:{x}}}{\:\sqrt{\mathrm{1}−\mathrm{cos}^{\mathrm{3}} \:{x}}}{dx}= \\…
Question Number 58791 by Tawa1 last updated on 30/Apr/19 $$\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}:\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\infty} \:\:\:\frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\:\:\:=\:\:\frac{\pi}{\mathrm{2}} \\ $$ Answered by tanmay last updated on 30/Apr/19 $${it}\:{has}\:{some}\:{trick}\:{to}\:{solve}… \\ $$$${F}\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 58774 by maxmathsup by imad last updated on 29/Apr/19 $${let}\:{f}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{d}\theta}{\mathrm{1}+{xtan}\theta}\:\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{tan}\theta}{\left(\mathrm{1}+{xtan}\theta\right)^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{let}\:{U}_{{n}} \left({x}\right)\:={f}^{\left({n}\right)} \left({x}\right)\:\:{give}\:{U}_{{n}}…
Question Number 58770 by Mr X pcx last updated on 29/Apr/19 $${find}\:{the}\:{value}\:{of}\:{integrals} \\ $$$$\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\:\:\:,\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Commented…
Question Number 189825 by TUN last updated on 22/Mar/23 $$\underset{{a}} {\int}^{{b}} \sqrt{\left({x}−{a}\right)\left({b}−{x}\right)}=¿ \\ $$ Answered by Frix last updated on 14/Apr/23 $$\mathrm{circle}: \\ $$$$\left({x}−\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} +{y}^{\mathrm{2}}…