Question Number 172818 by Mikenice last updated on 01/Jul/22 Answered by FelipeLz last updated on 02/Jul/22 $${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\:=\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \\ $$$${I}\:=\:\int\frac{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}}…
Question Number 172819 by Mikenice last updated on 01/Jul/22 Answered by CElcedricjunior last updated on 02/Jul/22 $$\int\boldsymbol{\mathrm{x}}^{\frac{\mathrm{3}}{\mathrm{2}}} \boldsymbol{\mathrm{arctan}}\left(\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} \right)\boldsymbol{\mathrm{dx}}=\boldsymbol{\mathrm{k}} \\ $$$$\left.\boldsymbol{\mathrm{posons}}\:\right)\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} =\boldsymbol{\mathrm{a}}=>\boldsymbol{\mathrm{dx}}=\boldsymbol{\mathrm{ada}} \\ $$$$\boldsymbol{\mathrm{k}}=\int\boldsymbol{\mathrm{a}}^{\mathrm{4}} \boldsymbol{\mathrm{arctan}}\left(\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{da}}…
Question Number 172784 by dragan91 last updated on 01/Jul/22 Answered by Eulerian last updated on 01/Jul/22 $$\: \\ $$$$\:\mathrm{Using}\:\mathrm{King}\:\mathrm{rule}\:\mathrm{of}\:\mathrm{integration}: \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{2006}} \:\mathrm{arctan}\left(\frac{\left(\mathrm{2007}−\mathrm{x}\right)\:−\:\mathrm{arctan}\left(\mathrm{2007}−\mathrm{x}\right)}{\mathrm{x}\:−\:\mathrm{arctan}\left(\mathrm{x}\right)}\right)\:\mathrm{dx} \\ $$$$\:=\:\int_{\mathrm{1}}…
Question Number 107245 by mnjuly1970 last updated on 09/Aug/20 $$\:\:\:\:\:\:\:\:\clubsuit\:\mathscr{Q}{uestion}\clubsuit \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{W}{hy}\:??? \\ $$$$….\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{\frac{\left(\mathrm{2}^{{x}} −\mathrm{1}\right){sin}^{\mathrm{3}} \left({x}\right)}{\left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left({sin}^{\mathrm{3}} \left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)\right)}\:}<\frac{\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:….\mathscr{M}.\mathscr{N}…. \\ $$…
Question Number 107238 by bemath last updated on 09/Aug/20 $$\:\:\:\:\:\:\:\boxplus{bemath}\boxplus \\ $$$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x}}\:{dx}\:?\: \\ $$ Answered by john santu last updated on 09/Aug/20 $$\:\:\:\:\divideontimes\mathrm{JS}\divideontimes…
Question Number 41702 by abdo.msup.com last updated on 11/Aug/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{3}}} \:{arcsin}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right){dt} \\ $$ Commented by math khazana by abdo last updated on 12/Aug/18…
Question Number 41703 by abdo.msup.com last updated on 11/Aug/18 $${calculate}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{cosx}}{{cos}^{\mathrm{3}} {x}\:+{sin}^{\mathrm{3}} {x}}{dx} \\ $$ Commented by math khazana by abdo last updated on…
Question Number 172767 by mathlove last updated on 01/Jul/22 $$\Phi=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\left(−\mathrm{1}\right)^{\frac{\mathrm{1}}{{x}}} }{{x}}\right){dx}=? \\ $$ Commented by mr W last updated on 01/Jul/22 $${Q}\mathrm{172653} \\…
Question Number 172764 by Mathematification last updated on 01/Jul/22 $$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\mathrm{x}}\right)^{\mathrm{2}} \:\mathrm{dx}=\:? \\ $$ Answered by Mathspace last updated on 01/Jul/22 $$\Upsilon=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}}…
Question Number 41679 by math khazana by abdo last updated on 11/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{t}\:+{xt}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{then}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{t}\:+{t}^{\mathrm{2}} \right){dt} \\…