Question Number 105700 by john santu last updated on 31/Jul/20 $$\underset{−\pi} {\overset{\pi} {\int}}\:\frac{{x}^{\mathrm{2}} \:{dx}}{\mathrm{1}+\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)+\sqrt{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{sin}\:{x}\right)}} \\ $$$$ \\ $$ Answered by bramlex last updated on…
Question Number 40161 by maxmathsup by imad last updated on 16/Jul/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}{{ln}\left(\mathrm{1}+\sqrt{{x}}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 40160 by maxmathsup by imad last updated on 16/Jul/18 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\mathrm{1}−{e}^{−{t}} }{{t}\sqrt{{t}}}\:{dt} \\ $$ Commented by math khazana by abdo last updated…
Question Number 40158 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \:{ln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{justify}\:{the}\:{existence}\:{of}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}+\mathrm{1}} \:−{A}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right)\:{prove}\:{that}\:\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\:\:\right.…
Question Number 40159 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} } \\ $$$${find}\:{a}\:{relation}\:{etween}\:{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{1}\:} \:{and}\:{I}_{\mathrm{2}} \\ $$…
Question Number 40157 by maxmathsup by imad last updated on 16/Jul/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:−\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 40154 by maxmathsup by imad last updated on 16/Jul/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 40155 by maxmathsup by imad last updated on 16/Jul/18 $${caoculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{t}\:{dt}}{\left(\mathrm{1}+{t}^{\mathrm{4}} \right)^{\mathrm{2}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 40156 by maxmathsup by imad last updated on 16/Jul/18 $${find}\:\:\:\int_{{e}^{\mathrm{2}} } ^{+\infty} \:\:\:\:\frac{{dt}}{{tln}\left({t}\right){ln}\left({ln}\left({t}\right)\right.} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 40153 by maxmathsup by imad last updated on 16/Jul/18 $${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\frac{{t}−\mathrm{2}}{\:\sqrt{{t}^{\mathrm{2}} \:−\mathrm{1}}}{dt} \\ $$ Commented by maxmathsup by imad last updated on…