Question Number 61884 by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{f}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} +{x}\:\:+{a}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\:\:{a}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convervenge}\:{of}\:\Sigma\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{also}\:{g}_{{n}}…
Question Number 61874 by aliesam last updated on 10/Jun/19 $$\int\frac{{xln}\left({x}\right)−{x}}{{ln}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$ Commented by Prithwish sen last updated on 10/Jun/19 $$\int\left[\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{2}} }\:−\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} }\:\right]\mathrm{dx} \\…
Question Number 127405 by john_santu last updated on 29/Dec/20 $$\:\mu\:=\:\int\:\frac{{x}^{\mathrm{7}} }{{x}^{\mathrm{10}} +\mathrm{169}}\:{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192933 by mnjuly1970 last updated on 31/May/23 Answered by MM42 last updated on 01/Jun/23 $${ln}\left(\mathrm{1}−{x}\right)={u}\Rightarrow\frac{−\mathrm{1}}{\mathrm{1}−{x}}{dx}={du}\:\:\&{i}\:{x}^{{n}−\mathrm{1}} {dx}={dv}\Rightarrow\frac{{x}^{{n}} }{{n}}={v} \\ $$$$\Rightarrow{I}_{{n}} =\int{x}^{{n}−\mathrm{1}} {ln}\left(\mathrm{1}−{x}\right){dx}=\frac{{x}^{{n}} {ln}\left(\mathrm{1}−{x}\right)}{{n}}\:+\frac{\mathrm{1}}{{n}}\int\:\frac{{x}^{{n}} }{\mathrm{1}−{x}}{dx}…
Question Number 61855 by aliesam last updated on 10/Jun/19 $$\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx} \\ $$ Answered by MJS last updated on 10/Jun/19 $$\frac{\mathrm{3}{x}^{\mathrm{3}}…
Question Number 192916 by Mingma last updated on 31/May/23 Answered by ARUNG_Brandon_MBU last updated on 31/May/23 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−\mathrm{sin2}{x}}{\mathrm{1}+\mathrm{cos}{x}}+\frac{\mathrm{1}−\mathrm{cos2}{x}}{\mathrm{1}+\mathrm{sin}{x}}\right){dx} \\ $$$$\:\:\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\mathrm{cos}{x}}+\mathrm{2}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}{x}}{\mathrm{1}+\mathrm{cos}{x}}\left(\mathrm{sin}{xdx}\right)+\mathrm{2}\int_{\mathrm{0}}…
Question Number 61842 by psyche last updated on 10/Jun/19 $$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{space}}\:\boldsymbol{{P}}{n}\:\boldsymbol{{with}}\:\boldsymbol{{H}}=\left\{{f}:{f}\subset{Pn}\:\boldsymbol{{and}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\partial{x}=\mathrm{0}\right\}\:.\:{S}\boldsymbol{{how}}\:\boldsymbol{{that}}\:\boldsymbol{{H}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{S}}{UBSPACE}\:{of}\:{Pn}. \\ $$ Commented by arcana last updated on 10/Jun/19 $$\mathrm{define}\:\mathrm{P}_{{n}} \\ $$ Terms…
Question Number 127377 by I want to learn more last updated on 29/Dec/20 Commented by zdf last updated on 29/Dec/20 $$ \\ $$ Commented by…
Question Number 127370 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:…\:\:{advanced}\:\:{calculus}\:\:.. \\ $$$$\:\:{prove}:: \\ $$$$\:\:\:\frac{\mathrm{1023}}{\mathrm{134}}\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{\frac{\mathrm{2}}{\mathrm{5}}} +{x}^{\frac{−\mathrm{2}}{\mathrm{5}}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{1024}{x}^{\mathrm{2}} \right)}{dx}=\frac{\pi}{\varphi} \\ $$$$\:\:\:\varphi:\:{golden}\:\:{ratio}… \\ $$$$ \\…
Question Number 127368 by I want to learn more last updated on 29/Dec/20 $$\int\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}} \mathrm{x}\:\:−\:\:\mathrm{1}}}\:\:\mathrm{dx} \\ $$ Answered by liberty last updated on 29/Dec/20 $$\:{let}\:\rightarrow\begin{cases}{\mathrm{tan}\:{x}\:\geqslant\mathrm{0}}\\{\mathrm{tan}^{\mathrm{2}}…