Question Number 66794 by mathmax by abdo last updated on 19/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{arctan}\left(\mathrm{2}{x}\right)\right)}{\mathrm{9}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66792 by mathmax by abdo last updated on 19/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left(\mathrm{2}\:{arctan}\left({x}\right)\right){dx} \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19…
Question Number 66795 by mathmax by abdo last updated on 19/Aug/19 $${let}\:{f}\left({x}\right)\:={e}^{−{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by mathmax by…
Question Number 66790 by mathmax by abdo last updated on 19/Aug/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}}{{sh}\left({x}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66793 by mathmax by abdo last updated on 19/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left(\mathrm{3}{arctanx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132324 by mnjuly1970 last updated on 13/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:{evaluation}\:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}\:^{\:\:} } ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx} \\ $$$$\:\:\:\:{solution}: \\ $$$$\:\:\boldsymbol{\phi}=\left[\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}=\boldsymbol{\phi}_{\mathrm{1}}…
Question Number 66786 by mathmax by abdo last updated on 19/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}}{{ch}\left({x}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19…
Question Number 66787 by mathmax by abdo last updated on 19/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2}} }{{ch}\left({x}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132301 by mnjuly1970 last updated on 13/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\:{nice}…….{calculus}…. \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:\:{that}\::: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left(\mathrm{2}{arctan}\left(\frac{{x}}{\mathrm{2}}\right)\right)}{\left({x}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \right){sinh}\left(\pi{x}\right)}{dx}=\frac{\mathrm{7}}{\mathrm{8}}\:−\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$$$ \\ $$ Terms of…
Question Number 132302 by Lordose last updated on 13/Feb/21 $$\boldsymbol{\mathrm{Simplify}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{\Gamma}\left(\frac{\boldsymbol{\mathrm{p}}}{\mathrm{2}}\right)\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\boldsymbol{\Gamma}\left(\frac{\boldsymbol{\mathrm{p}}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$ Answered by Ar Brandon last updated on 13/Feb/21 $$\Gamma\left(\mathrm{m}\right)\Gamma\left(\mathrm{m}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}}{\mathrm{2}^{\mathrm{2m}−\mathrm{1}} }\Gamma\left(\mathrm{2m}\right) \\…