Category: Integration

Question Number 27805 by abdo imad last updated on 15/Jan/18 $${find}\:\:\int_{\mathrm{1}} ^{\propto} \:\:\frac{{arctan}\left(\alpha{x}\right)}{{x}^{\mathrm{2}} }\:. \\ $$ Commented by abdo imad last updated on 16/Jan/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{1}}…

Question Number 27802 by abdo imad last updated on 15/Jan/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{2}{x}^{\mathrm{2}} } }{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo imad last updated…

Question Number 27797 by abdo imad last updated on 14/Jan/18 $${find}\:\:\:\int\:\sqrt{\mathrm{2}+{tan}^{\mathrm{2}} {t}}\:\:{dt}. \\ $$ Commented by abdo imad last updated on 19/Jan/18 $${let}\:{put}\:\:{I}=\:\int\sqrt{\mathrm{2}+{tan}^{\mathrm{2}} {t}}{dt}\:\:\:\: \\…

Question Number 27794 by abdo imad last updated on 14/Jan/18 $${let}\:{give}\:\:{I}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} {ln}\:\left(\mathrm{1}−\mathrm{2}{x}\:{cost}\:+{x}^{\mathrm{2}} \right){dt}\:{by}\:{using}\:{the} \\ $$$${polynomial}\:{p}\left({x}\right)=\:\left({z}+{x}\right)^{\mathrm{2}{n}} −\mathrm{1}\:\:{find}\:{the}\:{value}\:{of}\:{I}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 27781 by abdo imad last updated on 14/Jan/18 $${find}\:{the}\:{value}\:{of}\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{ln}\left(\mathrm{1}+{x}\:{sin}^{\mathrm{2}} {t}\right)}{{sin}^{\mathrm{2}} {t}}\:{dt}\:{knowing}\:{that} \\ $$$$−\mathrm{1}<{x}<\mathrm{1}\:. \\ $$ Commented by abdo imad last updated…