Question Number 42086 by maxmathsup by imad last updated on 17/Aug/18 $${let}\:\:\:\:{f}\left({x}\right)\:\:=\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{2}{xsh}\left({t}\right)\:+\mathrm{1}}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{1}+{sh}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{3}{sh}\left({t}\right)\:+\mathrm{1}}{dt}\:. \\…
Question Number 42087 by maxmathsup by imad last updated on 17/Aug/18 $${find}\:\:\:\:\int\:\:\:\:\:\:\:\:\frac{{x}\:{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 42083 by maxmathsup by imad last updated on 17/Aug/18 $${calculate}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\mathrm{3}+\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173149 by mnjuly1970 last updated on 07/Jul/22 $$ \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\:\:\infty} \frac{\:{dx}}{\:\sqrt{\mathrm{1}+{x}}\:.\left(\mathrm{2}+\mathrm{2}{x}\:+{x}^{\:\mathrm{2}} \right)}=\frac{\mathrm{1}}{\sigma}\:\left(\pi−\mathrm{ln}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{3}}\:\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sigma\:=\:? \\ $$$$\:\:\:\:\:\:\:\:−−\:\:\mathrm{solution}\:−− \\ $$$$\:\:\:\:\:\Omega\overset{\sqrt{\mathrm{1}+{x}}\:={t}} {=}\:\mathrm{2}\int_{\mathrm{0}} ^{\:\infty} \frac{{dt}}{\:\mathrm{1}+\:{t}^{\:\mathrm{4}} }\:=\:\mathrm{2}\int_{\mathrm{0}}…
Question Number 173150 by Frix last updated on 07/Jul/22 $$\mathrm{let}\:\forall{n}\in\mathbb{N}:\:{I}_{{n}} \left({f}\left({x}\right)\right)=\:\mathrm{the}\:{n}^{\mathrm{th}} \:\mathrm{antiderivate} \\ $$$$\mathrm{of}\:{f}\left({x}\right)\:\mathrm{with}\:{I}_{\mathrm{0}} ={f}\left({x}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{the}\:\mathrm{constants}\:{a}_{{n}} ,\:{b}_{{n}} \:\mathrm{of} \\ $$$${I}_{{n}} \left(\mathrm{ln}\:{x}\right)={a}_{{n}} {x}^{{n}} \mathrm{ln}\:{x}\:+{b}_{{n}} {x}^{{n}}…
Question Number 173148 by JordanRoddy last updated on 07/Jul/22 $$ \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{n}} \sqrt{\mathrm{x}}\:\left(\mathrm{arcsin}\:\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 173139 by mnjuly1970 last updated on 07/Jul/22 Answered by Mathspace last updated on 07/Jul/22 $$\Upsilon=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)} \\ $$$${changement}\:\sqrt{\mathrm{1}+{x}}={t}\:{give} \\ $$$${x}={t}^{\mathrm{2}} −\mathrm{1}\:\Rightarrow…
Question Number 107596 by Rio Michael last updated on 11/Aug/20 $$\mathrm{Given}\: \\ $$$$\:{I}_{{m},{n}} \:=\:\underset{\mathrm{1}} {\overset{{e}} {\int}}{x}^{{m}} \:\left(\mathrm{ln}\:{x}\right)^{{n}} \:{dx}\:\mathrm{where}\:{m},{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{1}\:+\:{m}\right){I}_{{m},{n}} \:=\:{e}^{{m}+\mathrm{1}} −{nI}_{{m},{n}−\mathrm{1}} \:\mathrm{for}\:{m}\:>\mathrm{0}\:\mathrm{and}\:{n}>\mathrm{0} \\ $$$$\mathrm{also},\:\mathrm{evaluate}\:{I}_{\mathrm{2},\mathrm{3}}…
Question Number 42054 by SammyKT last updated on 17/Aug/18 Commented by math khazana by abdo last updated on 17/Aug/18 $${what}\:{s}\:{C}?\:{C}\:{is}\:{not}\:{given}\:! \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 107591 by hgrocks last updated on 11/Aug/20 Commented by hgrocks last updated on 11/Aug/20 $$\mathrm{Pls}\:\mathrm{Tell}\:\mathrm{Me}\:\mathrm{Which}\:\mathrm{one}\:\mathrm{is}\:\mathrm{correct} \\ $$$$\mathrm{and}\:\mathrm{why}\: \\ $$ Commented by hgrocks last…