Question Number 133440 by bagjagunawan last updated on 22/Feb/21 Answered by Ar Brandon last updated on 22/Feb/21 $$\mathrm{f}\left({x}\right)={x}+\mathrm{5}+\sqrt{\mathrm{8}{x}}+\sqrt{\mathrm{12}{x}}+\sqrt{\mathrm{24}}\: \\ $$$$\:\:\:\:\:\:\:\:\:={x}+\left(\sqrt{\mathrm{8}}+\sqrt{\mathrm{12}}\right)\sqrt{{x}}+\mathrm{5}+\sqrt{\mathrm{24}}=\left(\sqrt{{x}}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$$\mathcal{I}=\int\mathrm{f}\left({x}\right)\mathrm{d}{x}=\int\sqrt{\left(\sqrt{{x}}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\mathrm{d}{x} \\ $$$$\:\:\:=\int\left(\sqrt{{x}}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\mathrm{d}{x}=\frac{\mathrm{2}}{\mathrm{3}}\sqrt{{x}^{\mathrm{3}}…
Question Number 133433 by greg_ed last updated on 22/Feb/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{4}} +\mathrm{1}}\:\boldsymbol{{dx}}, \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\::\:\mathrm{2}\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{4}} +\mathrm{1}}\:\boldsymbol{{dx}}. \\ $$ Answered by…
Question Number 133426 by metamorfose last updated on 22/Feb/21 $$\int\lfloor{x}\rfloor{dx}=?… \\ $$ Answered by MJS_new last updated on 22/Feb/21 $$\mathrm{for}\:{a}<{b}:\:\underset{{a}} {\overset{{b}} {\int}}\lfloor{x}\rfloor{dx}=\lfloor{a}\rfloor\underset{{a}} {\overset{\lceil{a}\rceil} {\int}}{dx}+\underset{\lceil{a}\rceil} {\overset{\lfloor{b}\rfloor−\mathrm{1}}…
Question Number 2340 by Yozzi last updated on 18/Nov/15 $${Prove}\:{that},\:\forall{m}\in\mathbb{Z}^{+} , \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{m}} {\prod}}\Gamma\left({x}+\frac{{r}−\mathrm{1}}{{m}}\right)={m}^{\frac{\mathrm{1}}{\mathrm{2}}−{mx}} \left(\mathrm{2}\pi\right)^{\frac{{m}−\mathrm{1}}{\mathrm{2}}} \Gamma\left({mx}\right). \\ $$$$\left\{\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {dt},\:{x}>\mathrm{0}\right\} \\ $$…
Question Number 67851 by mathmax by abdo last updated on 01/Sep/19 $${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C}\:. \\ $$ Commented by MJS last updated on 01/Sep/19 $$\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{problem}/\mathrm{mistake}\:\mathrm{if}\:\mathrm{we}\:\mathrm{just} \\ $$$$\mathrm{calculate}\:\mathrm{it}\:\mathrm{as}\:\mathrm{if}\:{z}\in\mathbb{R}?…
Question Number 67850 by mathmax by abdo last updated on 01/Sep/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 133369 by mnjuly1970 last updated on 21/Feb/21 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{calculus}\:\left(\mathrm{2}\right)….. \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{1}} ^{\:\mathrm{2}} \left(\frac{{ln}\left(\frac{{x}+\mathrm{2}}{{x}+\mathrm{1}}\right)}{{x}}\right){dx}\:=??? \\ $$$$ \\ $$ Commented by Dwaipayan Shikari last…
Question Number 67835 by mind is power last updated on 01/Sep/19 $$\int_{\mathrm{0}} ^{\mathrm{2}} {x}\left(\mathrm{8}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$ Answered by MJS last updated on 01/Sep/19…
Question Number 133360 by liberty last updated on 21/Feb/21 $$\int\:\sqrt{\mathrm{1}+\mathrm{sec}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Commented by som(math1967) last updated on 21/Feb/21 $$\int\sqrt{\frac{\mathrm{1}+{cosx}}{{cosx}}}{dx} \\ $$$$\sqrt{\mathrm{2}}\int\frac{{cos}\frac{{x}}{\mathrm{2}}}{\:\sqrt{\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}}{dx} \\ $$$$=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{2}}}\int\frac{{cos}\frac{{x}}{\mathrm{2}}}{\:\sqrt{\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}}…
Question Number 67823 by mhmd last updated on 31/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{lnx}+{e}^{{lnx}/{x}} } {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com