Question Number 60728 by Mr X pcx last updated on 25/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{ln}\left({lnx}\right)}{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60727 by Mr X pcx last updated on 25/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{ln}\left({lnx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 60716 by peter frank last updated on 24/May/19 Commented by maxmathsup by imad last updated on 25/May/19 $${let}\:{A}\left({x}\right)\:=\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{{x}} \:\Rightarrow{A}\left({x}\right)\:=\left(\mathrm{1}−\frac{{x}+\mathrm{1}}{{x}}\right)^{{x}} \:={e}^{{x}\:{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right)} \\ $$$${but}\:{we}\:{have}\:{for}\:{u}\:\in{V}\left(\mathrm{0}\right)\:{ln}\left(\mathrm{1}−{u}\right)\:\sim−{u}\:\Rightarrow{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right)\sim−\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{for}\:{x}\in{V}\left(+\infty\right) \\…
Question Number 126230 by I want to learn more last updated on 18/Dec/20 $$\int\:\boldsymbol{\mathrm{e}}^{\:\boldsymbol{\mathrm{cos}}^{−\:\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)} \:\:\:\mathrm{dx} \\ $$ Answered by Olaf last updated on 18/Dec/20…
Question Number 60692 by maxmathsup by imad last updated on 24/May/19 $${find}\:\:\int\:\:{arctan}\left(\mathrm{2}{cosx}\right){dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60691 by maxmathsup by imad last updated on 24/May/19 $${calculate}\:{f}\left({a}\right)\:=\:\int\:\:\:\left(\mathrm{1}−\frac{{a}}{{x}^{\mathrm{2}} }\right)\:{arctan}\left({x}+\frac{{a}}{{x}}\right){dx}\:\:\:{with}\:{a}\:{real}\:. \\ $$ Commented by maxmathsup by imad last updated on 27/May/19 $${by}\:{parts}\:\:{u}^{'}…
Question Number 60688 by maxmathsup by imad last updated on 24/May/19 $${find}\:\int\:\:\:{e}^{−{x}} \sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60690 by maxmathsup by imad last updated on 24/May/19 $${find}\:\int\:\left({x}+\mathrm{3}\right)\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60687 by maxmathsup by imad last updated on 24/May/19 $${calculate}\:\:\int\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\mathrm{2}{x}}\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/May/19…
Question Number 60685 by maxmathsup by imad last updated on 24/May/19 $${find}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}−{cos}\left({nx}\right)}{{sin}^{\mathrm{2}} \left({nx}\right)}{dx}\: \\ $$ Commented by maxmathsup by imad last updated…