Question Number 32044 by abdo imad last updated on 18/Mar/18 $${fimd}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\int_{\mathrm{0}} ^{{x}} \:{t}^{\mathrm{2}} \:{ln}\left(\mathrm{1}+{sint}\right)\:{dt}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 32043 by abdo imad last updated on 18/Mar/18 $${let}\:{f}\left({x}\right)=\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{dt}}{{lnt}}\:\:{with}\:{x}>\mathrm{0}\:{and}\:{x}\neq\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}>\mathrm{1}\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{xdt}}{{tlnt}}\:\leqslant{f}\left({x}\right)\leqslant\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{x}^{\mathrm{2}} {dt}}{{tlnt}}\:\:{after} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{1}}…
Question Number 163114 by abdullahhhhh last updated on 03/Jan/22 $$\int\left(\frac{\boldsymbol{\mathrm{cos}}\mathrm{5}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{cos}}\mathrm{4}\boldsymbol{\mathrm{x}}}{\mathrm{1}+\mathrm{2}\boldsymbol{\mathrm{cos}}\mathrm{3}\boldsymbol{\mathrm{x}}}\right)\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\: \\ $$ Answered by blackmamba last updated on 04/Jan/22 $$\:\int\:\frac{\frac{{e}^{\mathrm{5}{x}} +{e}^{−\mathrm{5}{x}} }{\mathrm{2}}\:+\frac{{e}^{\mathrm{4}{x}} +{e}^{−\mathrm{4}{x}}…
Question Number 32040 by abdo imad last updated on 18/Mar/18 $${let}\:{give}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+{x}\:{tant}}\:\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{tant}}{\left(\mathrm{1}+{xtant}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){give}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{tant}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{tant}\right)^{\mathrm{2}} }\:{dt}\:.…
Question Number 32039 by abdo imad last updated on 18/Mar/18 $${a}>−\mathrm{1}\:\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+{a}\:{tan}^{\mathrm{2}} {t}}\:. \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{tan}^{\mathrm{2}} {t}}{\left(\mathrm{1}+{atan}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{3}\right)\:\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{tan}^{\mathrm{2}}…
Question Number 163109 by mathmax by abdo last updated on 03/Jan/22 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{n}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{n}\:\mathrm{fromN}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{1}\right) \\ $$ Answered by mathmax by abdo last updated…
Question Number 32034 by abdo imad last updated on 18/Mar/18 $${let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\mathrm{1}+{x}+…+{x}^{{n}} }\:\:{study}\:{the}\:{convergence}\:{of} \\ $$$$\Sigma\:{u}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy…
Question Number 97569 by M±th+et+s last updated on 08/Jun/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{{tan}\left({x}\right)}\sqrt{\mathrm{1}−{tan}\left({x}\right)}\:{dx} \\ $$ Answered by MJS last updated on 08/Jun/20 $$\mathrm{use}\:\mathrm{thus}: \\ $$$${t}=\frac{\sqrt{\mathrm{1}−\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}\:{x}}}\:\rightarrow\:{dx}=−\mathrm{2cos}^{\mathrm{2}} \:{x}\sqrt{\mathrm{tan}^{\mathrm{3}}…
Question Number 32031 by abdo imad last updated on 18/Mar/18 $${let}\:\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{ax}} {ln}\left({x}\right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{ax}} \left({xlnx}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{x}}…
Question Number 32029 by abdo imad last updated on 18/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\alpha{x}} {ln}\left({x}\right)\:{dx}\:\:{with}\:\:\alpha>\mathrm{0}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com