Question Number 128851 by mnjuly1970 last updated on 10/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}\:\:\left({I}\right)… \\ $$$$\:\:\:{calculate}\:\::: \\ $$$$ \\ $$$$\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\left({e}−\mathrm{1}\right)\sqrt{{log}\left(\:\mathrm{1}+{ex}−{x}\:\right)}\:+{e}^{{x}^{\mathrm{2}} } \right\}{dx}=? \\ $$$$ \\ $$ Commented…
Question Number 128841 by mnjuly1970 last updated on 10/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:{calculus}\:… \\ $$$$\:\:\:\:\mathscr{E}{valuation}\:{of}\:::\:\Phi=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({x}\right).{arctan}\left({x}\right){dx} \\ $$$${solution}:: \\ $$$$\:\:\:\:{note}\:\mathrm{1}::\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{\mathrm{2}{n}−\mathrm{1}}={arctan}\left(\mathrm{1}\right)=\frac{\pi}{\mathrm{4}} \\ $$$${note}\:\mathrm{2}\:::\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}}…
Question Number 63292 by aliesam last updated on 02/Jul/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dy}}{\mathrm{1}+{y}\left({x}^{\mathrm{2}} −{x}\right)}\:{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 128826 by benjo_mathlover last updated on 10/Jan/21 $$\int_{−\mathrm{1}} ^{\:\mathrm{5}} \sqrt{\frac{\mathrm{2x}^{\mathrm{2}} −\mathrm{8}}{\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$ Answered by bobhans last updated on 10/Jan/21 $$\:\int\:\sqrt{\frac{\left({x}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} −\left(\sqrt{\mathrm{8}}\right)^{\mathrm{2}} }{{x}}}\:{dx}\:…
Question Number 63273 by mathmax by abdo last updated on 01/Jul/19 $${let}\:{F}\left({x}\right)\:=\int_{{x}^{\mathrm{2}} } ^{{x}^{\mathrm{3}} } \:\:\:\:\:\frac{{sin}\left({t}\right)}{{t}+{x}}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {F}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculste}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}^{'} \left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:{F}^{'}…
Question Number 63268 by aliesam last updated on 01/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128797 by mnjuly1970 last updated on 10/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\phi\:\overset{???} {=}\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{tanh}\left({x}\right)}{{e}^{{x}} }\right)\:{dx} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last…
Question Number 63261 by aliesam last updated on 01/Jul/19 $$\int{x}\:{tan}\left({x}\right)\:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 01/Jul/19 $${u}={tanx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={xdx}\Rightarrow{v}=\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\…
Question Number 63251 by Tawa1 last updated on 01/Jul/19 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{m}\:\mathrm{cos}\theta\right)\:\mathrm{d}\theta \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128775 by bramlexs22 last updated on 10/Jan/21 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{let}\:\varphi\:=\:\sqrt{\frac{\mathrm{1}+\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\Rightarrow\mathrm{x}\:=\:\frac{\varphi^{\mathrm{2}} −\mathrm{1}}{\varphi^{\mathrm{2}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{dx}\:=\:\frac{\mathrm{4}\varphi}{\left(\varphi^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}}…