Question Number 136858 by mathmax by abdo last updated on 27/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{sinx}\right)−\mathrm{sin}\left(\mathrm{cosx}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 71314 by mathmax by abdo last updated on 13/Oct/19 $${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 13/Oct/19…
Question Number 136844 by rs4089 last updated on 26/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136840 by physicstutes last updated on 26/Mar/21 $$\:\int\sqrt{\frac{{x}}{{x}−\mathrm{1}}}\:{dx} \\ $$ Answered by Olaf last updated on 26/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\sqrt{\frac{{x}}{{x}−\mathrm{1}}}\:{dx} \\ $$$$\mathrm{F}\left({u}\right)\:\overset{{x}={u}^{\mathrm{2}} } {=}\:\int\sqrt{\frac{{u}^{\mathrm{2}} }{{u}^{\mathrm{2}}…
Question Number 136841 by physicstutes last updated on 26/Mar/21 $$\int\sqrt{{x}^{\mathrm{2}} +\mathrm{1}\:}\:{dx}\:=\:? \\ $$ Answered by Olaf last updated on 26/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$\mathrm{F}\left({u}\right)\:\:\overset{{x}=\mathrm{sh}{u}} {=}\:\:\int\sqrt{\mathrm{sh}^{\mathrm{2}}…
Question Number 136835 by mnjuly1970 last updated on 26/Mar/21 $$\:\:\:\:\:\:\:\:…..{nice}\:\:\:\:\:{calculus}… \\ $$$$\:\:\:{for}\:\:\:\:{f}\left({x}\right)={f}\left({x}+\pi\right)\:: \\ $$$$\:\:\:\:\:\int_{−\infty} ^{\:\infty} {f}\left({x}\right).\frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}\overset{{why}???} {=}\int_{\mathrm{0}} ^{\:\pi} {f}\left({x}\right){dx} \\ $$ Terms of…
Question Number 136813 by mnjuly1970 last updated on 26/Mar/21 $$\:\:\:\:\: \\ $$$$\:\:\:……{advanced}\:\:\:\:{calculus}\left({I}\right)…. \\ $$$$\:\:\:\:{if}\::\: \\ $$$$\:\:\Omega=\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}.{cos}\left(\mathrm{2}{x}\right).{cos}\left({x}\right)}{{sin}^{\mathrm{7}} \left({x}\right)}\:{dx}=\frac{{a}\pi}{\mathrm{90}} \\ $$$$\:\:\:{then}\:\:::\:\:{a}=??? \\ $$$$\:\: \\ $$$$\:\:\:\:…
Question Number 136806 by mnjuly1970 last updated on 26/Mar/21 Answered by Dwaipayan Shikari last updated on 26/Mar/21 $$\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)}{\:\sqrt[{\mathrm{3}}]{{x}}}{dx}\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }={u}\Rightarrow−\frac{\mathrm{3}}{{x}^{\mathrm{4}} }=\frac{{du}}{{dx}} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\int_{\mathrm{0}}…
Question Number 136803 by mnjuly1970 last updated on 26/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…..\mathscr{A}{dvanced}\:\:\:\:\blacktriangleleft………….\blacktriangleright\:\:\:\mathscr{C}{alculus}….. \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:\infty} \frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)}{{x}}{dx}=……??? \\ $$$$\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\overset{\frac{\mathrm{1}}{{x}}\:={t}} {=}\:\mathrm{2}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}^{\mathrm{3}} \right)}{\frac{\mathrm{1}}{{t}}}.\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 71239 by 20190927 last updated on 13/Oct/19 $$\int\frac{\mathrm{1}}{\mathrm{2cosx}−\mathrm{5sinx}−\mathrm{3}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 13/Oct/19 $${let}\:{I}\:=\int\:\:\:\:\frac{{dx}}{\mathrm{2}{cosx}−\mathrm{5}{sinx}\:−\mathrm{3}}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}\:=\int\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…