Question Number 84956 by M±th+et£s last updated on 17/Mar/20 $${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)+\mathrm{1}}\:{dx}=\frac{\pi}{\mathrm{2}\phi} \\ $$ Commented by mathmax by abdo last updated…
Question Number 84942 by M±th+et£s last updated on 17/Mar/20 $$\int_{\mathrm{0}} ^{{x}} {sinh}\left({x}−{t}\right)\:{cosh}\left({t}\right)\:{dt} \\ $$ Answered by mind is power last updated on 17/Mar/20 $${sh}\left({x}\right){ch}\left({y}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left\{{sh}\left({x}+{y}\right)+{sh}\left({x}−{y}\right)\right\} \\…
Question Number 84894 by Power last updated on 17/Mar/20 Commented by abdomathmax last updated on 18/Mar/20 $${I}=\int\sqrt{\frac{{ax}+{b}}{{cx}+{d}}}{dx}\:{we}\:{do}\:{the}\:{changement}\sqrt{\frac{{ax}+{b}}{{cx}+{d}}}={t}\:\Rightarrow \\ $$$$\frac{{ax}+{b}}{{cx}+{d}}={t}^{\mathrm{2}} \:\Rightarrow{ax}+{b}={ct}^{\mathrm{2}} {x}\:+{dt}^{\mathrm{2}} \:\Rightarrow\left({a}−{ct}^{\mathrm{2}} \right){x}={dt}^{\mathrm{2}} −{b}\:\Rightarrow \\…
Question Number 84879 by sahnaz last updated on 17/Mar/20 $$\mathrm{e}^{\int\frac{\mathrm{2dx}}{\mathrm{xlnx}}} \\ $$ Commented by jagoll last updated on 17/Mar/20 $$\int\:\frac{\mathrm{2dx}}{\mathrm{x}\:\mathrm{lnx}}\:=\:\int\:\frac{\mathrm{2d}\left(\mathrm{lnx}\right)}{\mathrm{lnx}}\:=\:\int\:\mathrm{2}\frac{\mathrm{du}}{\mathrm{u}} \\ $$$$=\:\mathrm{2}\:\mathrm{ln}\:\mathrm{u}\:+\:\mathrm{c}\:,\:\left[\mathrm{u}\:=\:\mathrm{ln}\:\mathrm{x}\:\right] \\ $$$$=\:\mathrm{2ln}\left(\mathrm{lnx}\right)\:+\:\mathrm{2lnC}\:=\:\mathrm{2ln}\left(\mathrm{Clnx}\right) \\…
Question Number 84859 by M±th+et£s last updated on 16/Mar/20 $${show}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} …\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{n}}{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +…+{x}_{{n}} }{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} …{dx}_{{n}} =\mathrm{2}\: \\…
Question Number 84843 by M±th+et£s last updated on 16/Mar/20 $$\int\frac{{sin}\left(\mathrm{7}{x}\right)}{{cos}\left(\mathrm{3}{x}\right)}\:{dx} \\ $$ Commented by jagoll last updated on 17/Mar/20 $$\mathrm{sin}\:\mathrm{7x}\:=\:\mathrm{sin}\:\left(\mathrm{4x}+\mathrm{3x}\right)\: \\ $$$$=\:\mathrm{sin}\:\mathrm{4x}\:\mathrm{cos}\:\mathrm{3x}\:+\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{sin}\:\mathrm{3x} \\ $$$$\int\:\frac{\mathrm{sin}\:\mathrm{7x}}{\mathrm{cos}\:\mathrm{3x}}\:\mathrm{dx}\:=\:\int\:\left(\mathrm{sin}\:\mathrm{4x}\:+\:\mathrm{cos}\:\mathrm{4x}\:\mathrm{tan}\:\mathrm{3x}\right)\mathrm{dx} \\…
Question Number 150366 by SLVR last updated on 11/Aug/21 Commented by SLVR last updated on 11/Aug/21 $${kindly}\:{provide}\:{solution}..{already} \\ $$$${given}\:{in}\:{group} \\ $$ Terms of Service Privacy…
Question Number 150356 by mnjuly1970 last updated on 11/Aug/21 $$\:{solve}… \\ $$$$\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{Arcsin}\:\left(\sqrt{{x}}\:\right)}{\mathrm{1}−{x}\:+\:{x}^{\:\mathrm{2}} }\:{dx}=? \\ $$ Answered by Lordose last updated on 12/Aug/21 $$…
Question Number 84809 by M±th+et£s last updated on 16/Mar/20 $$\int\frac{{x}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} {arctan}\left({x}\right)}\:{dx} \\ $$ Commented by abdomathmax last updated on 18/Mar/20 $${A}\:=\int\:\:\:\:\frac{{x}}{\left({x}^{\mathrm{2}\:} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \:{arctanx}}\:{changement}\:{arctanx}={t} \\…
Question Number 84810 by M±th+et£s last updated on 16/Mar/20 $$\int_{\mathrm{0}} ^{\pi} {ln}\left(\frac{\mathrm{1}+{b}\:{cos}\left({x}\right)}{\mathrm{1}+{a}\:{sin}\left({x}\right)}\right)\:{dx} \\ $$$$−\mathrm{1}<{a}<{b}<\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 16/Mar/20…