Question Number 190009 by Rupesh123 last updated on 26/Mar/23 Commented by Frix last updated on 26/Mar/23 $$\mathrm{Use}\:{t}={x}^{\frac{\pi}{\mathrm{5}}} \:\mathrm{to}\:\mathrm{get}\:\frac{\mathrm{5}}{\pi}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{{t}^{\mathrm{10}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{now}\:“\mathrm{just}'' \\ $$$$\mathrm{decompose}\:\mathrm{etc}. \\ $$…
Question Number 58937 by Tony Lin last updated on 02/May/19 $$\int_{\mathrm{0}} ^{\mathrm{2}} \underset{\frac{\mathrm{1}}{{n}}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{2}−{x}\right)\left({x}+{x}^{{n}} \right)}{\mathrm{1}+{x}^{{n}} }{dx}=\:? \\ $$ Commented by maxmathsup by imad last updated…
Question Number 124452 by liberty last updated on 03/Dec/20 $$\:\mathrm{2}\:\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{1}}\:=\:{x}^{\mathrm{3}} −\mathrm{1}\: \\ $$ Commented by Dwaipayan Shikari last updated on 03/Dec/20 $${Golden}\:{ratio}\:\phi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}=\mathrm{1}.\mathrm{6180}.. \\ $$ Answered…
Question Number 124438 by Ar Brandon last updated on 03/Dec/20 $$\int\mathrm{e}^{\left(\mathrm{xsinx}+\mathrm{cosx}\right)} \centerdot\left(\frac{\mathrm{x}^{\mathrm{4}} \mathrm{cos}^{\mathrm{3}} \mathrm{x}−\mathrm{xsinx}+\mathrm{cosx}}{\mathrm{x}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \mathrm{x}}\right)\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 124432 by mnjuly1970 last updated on 03/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{find}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{4}} \frac{{ln}\left({x}\right)}{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{dx}=? \\ $$ Answered by mindispower last updated…
Question Number 124430 by benjo_mathlover last updated on 03/Dec/20 $$\:\int\overset{\:\mathrm{5}} {\:}_{\mathrm{0}} \frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\left(\mathrm{5}−{x}\right)^{\mathrm{2}} }\:{dx}\:=?\: \\ $$ Answered by liberty last updated on 03/Dec/20 $$\mu\:=\underset{\mathrm{0}}…
Question Number 124421 by Ar Brandon last updated on 03/Dec/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\mathrm{e}^{\mathrm{x}} \centerdot\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} }\mathrm{dx}=\frac{\mathrm{e}^{\mathrm{x}} \left\{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right\}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }+\mathrm{C} \\ $$ Commented by…
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…