Question Number 133973 by liberty last updated on 26/Feb/21 $$\:\mathrm{Given}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{27}}}}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{27}}}}}\\{\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} +\mathrm{x}+\mathrm{1}}\end{cases} \\ $$$$\mathrm{Find}\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{g}\circ\mathrm{f}\circ\mathrm{g}\right)\left(\mathrm{x}\right)\:\mathrm{dx}\:. \\ $$ Answered by EDWIN88 last updated on…
Question Number 68434 by mhmd last updated on 10/Sep/19 Answered by mind is power last updated on 10/Sep/19 $$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}=\int_{{a}} ^{{b}} {f}\left({a}+\mathrm{b}−\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{3sin}\left(\mathrm{x}\right)−\mathrm{2sin}^{\mathrm{2}}…
Question Number 133972 by liberty last updated on 26/Feb/21 $$\mathscr{H}\:=\:\int\:\frac{\left(\mathrm{2x}−\mathrm{1}\right)^{\mathrm{7}} }{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{9}} }\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 26/Feb/21 $$\:\mathscr{H}\:=\:\int\:\left(\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{2x}+\mathrm{1}}\right)^{\mathrm{7}} .\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{2}} } \\…
Question Number 133963 by bobhans last updated on 25/Feb/21 $$\mathcal{Y}\:=\:\int\:\frac{{dx}}{\:\sqrt[{\mathrm{6}}]{\mathrm{1}+{x}^{\mathrm{6}} }}? \\ $$ Answered by EDWIN88 last updated on 26/Feb/21 $$\mathbb{Y}=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}\:\sqrt[{\mathrm{6}}]{\mathrm{1}+\mathrm{x}^{−\mathrm{6}} }}\:=\:\int\:\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{x}^{\mathrm{7}} \:\sqrt[{\mathrm{6}}]{\mathrm{1}+\mathrm{x}^{−\mathrm{6}} }}\:\mathrm{dx}\:…
Question Number 133957 by mathmax by abdo last updated on 25/Feb/21 $$\left.\mathrm{1}\right)\mathrm{decompose}\:\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{2x}−\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\int_{\mathrm{1}} ^{\infty} \:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Olaf last updated…
Question Number 133951 by liberty last updated on 25/Feb/21 $$\:\mathcal{V}\:=\:\int\:\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)\:\mathrm{dx}\: \\ $$ Answered by mathmax by abdo last updated on 25/Feb/21 $$\Phi\:=\int\:\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}=\mathrm{sht}\:\Rightarrow \\…
Question Number 68409 by mathmax by abdo last updated on 10/Sep/19 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 133943 by mnjuly1970 last updated on 25/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:\:\:\:\:{calculus}…… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({x}^{\mathrm{2}} \right)−{cos}\left({x}\right)}{{x}}{dx}=\frac{\gamma}{\mathrm{2}} \\ $$$$\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant}… \\ $$ Terms of Service Privacy…
Question Number 133938 by Algoritm last updated on 25/Feb/21 Answered by mathmax by abdo last updated on 25/Feb/21 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(−\mathrm{lnx}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{changement}\:−\mathrm{lnx}=\mathrm{t}\:\mathrm{give}\:\mathrm{x}=\mathrm{e}^{−\mathrm{t}} \:\Rightarrow \\ $$$$\mathrm{I}=\int_{\mathrm{0}}…
Question Number 133911 by liberty last updated on 25/Feb/21 $$\mathcal{A}=\int\:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{5x}+\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by Ar Brandon last updated on 25/Feb/21 $$\mathcal{A}=\int\frac{\mathrm{cosx}}{\mathrm{sin5x}+\mathrm{sinx}}\mathrm{dx}=\int\frac{\mathrm{cosx}}{\mathrm{2sin3xcos2x}}\mathrm{dx} \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{cosx}\:\mathrm{dx}}{\left(\mathrm{3sinx}−\mathrm{4sin}^{\mathrm{3}} \mathrm{x}\right)\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \mathrm{x}\right)}…