Question Number 136883 by bramlexs22 last updated on 27/Mar/21 $$\mathrm{Given}\:\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{7}^{{a}} −\mathrm{2}\right)=\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}^{{a}} +\mathrm{2}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\int_{{a}} ^{\mathrm{e}} \:\frac{\mathrm{1}+\mathrm{ln}\:\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{x}} +\mathrm{x}^{−\mathrm{x}} }\:\mathrm{dx}\:. \\ $$ Answered by Olaf…
Question Number 5800 by sumit last updated on 28/May/16 $$\int\frac{{cos}\mathrm{2}{x}}{{sin}^{\mathrm{2}} {x}\centerdot{cos}^{\mathrm{2}} {x}}{dx} \\ $$$$ \\ $$ Commented by Boma last updated on 09/Aug/19 Boma Answered…
Question Number 136868 by mnjuly1970 last updated on 27/Mar/21 $$\:\:\:\:\:\:\:\:\:……\:{nice}\:\:\:\:\:{calculus}…. \\ $$$$\:\:{prove}\:\:{that}\::: \\ $$$$\:{i}:\:\:\int_{−\infty} ^{\:\infty} \frac{{dx}}{\left(\mathrm{1}+{x}+{e}^{{x}} \right)^{\mathrm{2}} +\pi^{\mathrm{2}} }\:=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\:{ii}:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({tan}\left({x}\right)\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{{e}}\right) \\ $$$$\:\:\:\:\:…
Question Number 136859 by mathmax by abdo last updated on 27/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{cosx}\right)−\mathrm{sin}\left(\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136858 by mathmax by abdo last updated on 27/Mar/21 $$\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…