Question Number 96034 by M±th+et+s last updated on 29/May/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{x}^{\mathrm{10}} +\mathrm{1}}{dx}=\frac{\mathrm{2}\pi}{\mathrm{5}\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)}=\frac{\pi\phi}{\mathrm{5}} \\ $$ Commented by M±th+et+s last updated on 30/May/20 $${thanks}\:{for}\:{solutions} \\ $$…
Question Number 30500 by abdo imad last updated on 22/Feb/18 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{2}} \left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30498 by abdo imad last updated on 22/Feb/18 $${find}\:\:{I}=\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{3}}} \:{arcsin}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}\:\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $${by}\:{part}\:\: \\…
Question Number 30499 by abdo imad last updated on 22/Feb/18 $${let}\:{put}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\sqrt{{tant}}\:\:{dt}\:{with}\:{x}>\mathrm{0}\:\:{find}\:{F}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30494 by abdo imad last updated on 22/Feb/18 $${find}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $${x}={sinh}\left({t}\right)\Rightarrow{dx}={cosh}\left({t}\right){dt}=\sqrt{\mathrm{1}+{sinh}^{\mathrm{2}} {t}}{dt}…
let-f-x-k-2-1-k-x-k-1-find-D-f-2-let-put-x-n-1-1-n-n-x-Rieman-alternate-serie-find-f-x-interms-of-x-
Question Number 30480 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\:\sum_{{k}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{x}+{k}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){let}\:{put}\:\delta\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{{x}} }\:\:\left({Rieman}\:{alternate}\:{serie}\right) \\ $$$${find}\:{f}\left({x}\right)\:{interms}\:{of}\:\delta\left({x}\right). \\…
Question Number 30478 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:\:{l}_{{i}} \left({x}\right)=\:\int_{\mathrm{2}} ^{{x}} \:\:\:\frac{{dt}}{{ln}\left({t}\right)}\:{find}\:{a}\:{serie}\:{equal}\:{to}\:{l}_{{i}} \left({x}\right). \\ $$$${x}\geqslant\mathrm{2}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30477 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:\mathrm{2}\left(×\right)\:{derivable}\:{prove}\:{that} \\ $$$${L}\left({f}^{'} \right)=\:{pL}\left({f}\right)\:−{f}\left({o}\right)\:{and}\:{L}\left({f}^{''} \right)={p}^{\mathrm{2}} {L}\left({f}\right)−{pf}\left(\mathrm{0}\right)−{f}^{'} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{let}\:{f}\left({t}\right)={tsin}\left({wt}\right)\:{find}\:{L}\left({f}\right). \\ $$ Terms of Service Privacy…
Question Number 30475 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\frac{{sin}\left({xt}\right)}{{t}}\:{e}^{−{t}} \:{dt} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow\infty} {f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{another}\:{form}\:{of}\:{f}_{{n}} \left({x}\right)\:{by}\:{calculating}\:{f}_{{n}} ^{'} \left({x}\right). \\…
Question Number 30476 by abdo imad last updated on 22/Feb/18 $${find}\:{L}\left({cos}^{\mathrm{2}} {x}\right)\:{and}\:{L}\left({sin}^{\mathrm{2}} {x}\right)\:{L}\:{is}\:{laplace}\:{transform}. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $${L}\left({cos}^{\mathrm{2}} {x}\right)={L}\left(\frac{{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left({L}\left({cos}\left(\mathrm{2}{x}\right)\right)+{L}\left(\mathrm{1}\right)\right) \\…