Question Number 145200 by qaz last updated on 03/Jul/21 $$\mathrm{evaluate}::\:\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=\frac{\mathrm{e}}{\mathrm{2}} \\ $$ Answered by mindispower last updated on 03/Jul/21 $${n}^{\mathrm{4}} +{n}^{\mathrm{2}}…
Question Number 145202 by mnjuly1970 last updated on 03/Jul/21 Commented by loveineq last updated on 03/Jul/21 $$\mathrm{Wow},\:\mathrm{it}\:\mathrm{likes}\:\mathrm{a}\:\mathrm{therom}. \\ $$ Answered by ajfour last updated on…
Question Number 145184 by mathmax by abdo last updated on 03/Jul/21 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{sin}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)−\mathrm{sh}\left(\mathrm{sin}\left(\mathrm{3x}\right)\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 79646 by abdomathmax last updated on 27/Jan/20 $${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left({narcosx}\right){dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$ Commented by abdomathmax last updated on 12/Mar/20 $${changement}\:{arcosx}={t}\:{give}\:{x}={cost}\:\Rightarrow…
Question Number 145183 by mathmax by abdo last updated on 03/Jul/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{x}}+\sqrt{\mathrm{x}+\mathrm{1}}\right)^{\mathrm{3}} } \\ $$ Commented by justtry last updated on 03/Jul/21 Answered…
Question Number 79645 by abdomathmax last updated on 27/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 79634 by TawaTawa last updated on 26/Jan/20 Commented by mathmax by abdo last updated on 27/Jan/20 $$\Omega\:=\int_{\frac{\pi}{\mathrm{5}}} ^{\frac{\mathrm{3}\pi}{\mathrm{10}}} \:\frac{{x}}{{sin}\left(\mathrm{2}{x}\right)}{dx}\:\:{changement}\:{x}=\frac{\pi}{\mathrm{2}}−{t}\:{givet}=\frac{\pi}{\mathrm{2}}−{x} \\ $$$$\Omega=\int_{\frac{\mathrm{3}\pi}{\mathrm{10}}} ^{\frac{\pi}{\mathrm{5}}} \:\frac{\frac{\pi}{\mathrm{2}}−{t}}{{sin}\left(\mathrm{2}{t}\right)}\left(−{dt}\right)\:=\frac{\pi}{\mathrm{2}}\int_{\frac{\pi}{\mathrm{5}}}…
Question Number 79627 by mathmax by abdo last updated on 26/Jan/20 $$\left.\mathrm{1}\right)\:{expicite}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 79615 by M±th+et£s last updated on 26/Jan/20 $${prove}\:{that}\:{with}\:{using}\:{hypergeometric}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left({x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{3}} }{\mathrm{3}}\:\mathrm{1}{F}_{\mathrm{2}} \left[\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{7}}{\mathrm{4}};\frac{−\pi^{\mathrm{4}} }{\mathrm{4}}\right]\: \\ $$ Commented by mind is power…
Question Number 79612 by john santu last updated on 26/Jan/20 $$\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}\:}\left(\sqrt[{\mathrm{4}\:}]{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{10}} }\:=\:? \\ $$ Answered by MJS last updated on 26/Jan/20 $$\int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \left({x}^{\frac{\mathrm{1}}{\mathrm{4}}} +\mathrm{1}\right)^{\mathrm{10}} }=…