Question Number 150533 by mnjuly1970 last updated on 13/Aug/21 $$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{solve}… \\ $$$$\:\:\mathrm{I}:=\:\int_{−\infty} ^{\:\infty} {e}^{\:{x}−{n}.{sinh}^{\:\mathrm{2}} \left({x}\right)} {dx}\:\overset{??} {=}\sqrt{\frac{\pi}{{n}}} \\ $$$$\:\:\:\:\:\:\:…{m}.{n}… \\ $$ Answered by…
Question Number 19457 by NEC last updated on 11/Aug/17 $${prove}\:{that}\:\int\mathrm{tan}\:^{\mathrm{2}} {xdx} \\ $$$$ \\ $$$$=\mathrm{tan}\:{x}−{x} \\ $$ Answered by Joel577 last updated on 11/Aug/17 $$\int\:\mathrm{tan}^{\mathrm{2}}…
Question Number 84958 by M±th+et£s last updated on 17/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84957 by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{2}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} \:\mathrm{dx}\:=\: \\ $$ Commented by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{8}−\mathrm{3}\left(\mathrm{4x}^{\mathrm{2}} \right)+\mathrm{3}\left(\mathrm{2x}^{\mathrm{4}}…
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} \\…