Question Number 206568 by universe last updated on 18/Apr/24 Answered by Berbere last updated on 19/Apr/24 $$\frac{{x}}{{n}}={y}\:\:{A}\left({n}\right)=\int_{\mathrm{0}} ^{{n}} \left(\frac{\mathrm{2}{nx}}{{x}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right)^{{n}} {dx}={n}\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\mathrm{2}{y}}{\mathrm{1}+{y}^{\mathrm{2}} }\right)^{{n}}…
Question Number 206537 by necx122 last updated on 18/Apr/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$ Answered by Berbere last updated on 18/Apr/24 $$=\int\frac{{x}\left(\mathrm{4}{x}^{\mathrm{3}} +\mathrm{2}{x}\right)−\mathrm{2}{x}^{\mathrm{4}}…
Question Number 206489 by Simurdiera last updated on 16/Apr/24 $${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$ Answered by Frix last updated on 16/Apr/24 $${t}=\mathrm{tan}\:{x} \\…
Question Number 206490 by Simurdiera last updated on 16/Apr/24 $${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$ Answered by Frix last updated on 16/Apr/24 $${t}=\mathrm{tan}\:{x} \\…
Question Number 206338 by mnjuly1970 last updated on 12/Apr/24 Answered by Sorena last updated on 12/Apr/24 $$\left[{x}\right]−\left[{x}^{\mathrm{2}} \right]\geqslant\mathrm{0}\:\rightarrow\:\left[{x}\right]\geqslant\left[{x}^{\mathrm{2}} \right]\:\rightarrow\:{x}\in\left[\mathrm{0},\sqrt{\mathrm{2}}\right) \\ $$ Terms of Service Privacy…
Question Number 206248 by MetaLahor1999 last updated on 10/Apr/24 $$\int\frac{\mathrm{1}}{\:\sqrt{\left(\mathrm{1}−{t}\right)\left(\mathrm{2}−{t}\right)}}{dt}=…? \\ $$ Answered by TonyCWX08 last updated on 10/Apr/24 $$\int\frac{\mathrm{1}}{\:\sqrt{{t}^{\mathrm{2}} −\mathrm{3}{t}+\mathrm{2}}}{dt} \\ $$$$=\int\frac{\mathrm{1}}{\:\sqrt{\left({t}−\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}}}{dt} \\…
Question Number 206200 by Shrodinger last updated on 09/Apr/24 $$\int\frac{{xsinx}}{\mathrm{1}−{cosx}}{dx} \\ $$ Answered by Frix last updated on 09/Apr/24 $$\int\frac{{x}\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}{dx}=\mathrm{i}\int\frac{{x}\left(\mathrm{e}^{\mathrm{i}{x}} +\mathrm{1}\right)}{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{1}}{dx}= \\ $$$$=\mathrm{i}\int{xdx}+\mathrm{2i}\int\frac{{x}}{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{1}}{dx}…
Question Number 206224 by mathzup last updated on 09/Apr/24 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{5}} \right){dx} \\ $$ Answered by Frix last updated on 10/Apr/24 $$\int\mathrm{tan}^{−\mathrm{1}} \:{x}^{{n}} \:{dx}\:\underset{{u}'=\mathrm{1}\wedge{v}=\mathrm{tan}^{−\mathrm{1}}…
Question Number 206078 by universe last updated on 06/Apr/24 Commented by TheHoneyCat last updated on 10/Apr/24 Can you please give an explicit formula for the a_n please? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 206072 by MetaLahor1999 last updated on 06/Apr/24 $$\int_{\mathrm{0}} ^{\pi} {arctan}\left(\frac{{ln}\left({sin}\left({x}\right)\right)}{{x}}\right){dx}=…? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com