Question Number 119006 by A8;15: last updated on 21/Oct/20 Answered by Dwaipayan Shikari last updated on 21/Oct/20 $$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}={I} \\ $$$$=\int_{\mathrm{2}} ^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 53471 by maxmathsup by imad last updated on 22/Jan/19 $$\left.\mathrm{1}\right){find}\:\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{tan}^{{n}} {tdt}\:\:\:{with}\:{n}\:{integr}\:. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \\ $$$$…
Question Number 53470 by maxmathsup by imad last updated on 22/Jan/19 $${find}\:\:{Vn}=\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{{an}−\mathrm{1}}{{n}}} \:\frac{\sqrt{{x}}}{\:\sqrt{{a}−\sqrt{{x}}+{x}}}{dx} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated…
Question Number 53467 by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{A}_{{n}\:{m}} \:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \left(\mathrm{1}−{x}\right)^{{m}} {dx}\:\:{with}\:{n}\:{and}\:{n}\:{integrs}\:{naturals} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}\:{m}} \:\:{by}\:{using}\:{factoriels} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n},{m}} \:{A}_{{nm}} \\ $$…
Question Number 53465 by maxmathsup by imad last updated on 22/Jan/19 $${find}\:\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{{cosx}\:−{cos}^{\mathrm{3}} {x}}{dx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 53463 by maxmathsup by imad last updated on 22/Jan/19 $$\left.\mathrm{1}\right){let}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}}\:\:\:\:{and}\:\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{sin}\theta\:{x}\:+\mathrm{1}}} \\ $$$${calculate}\:{A}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+\sqrt{\mathrm{2}}{x}\:+\mathrm{1}}} \\ $$ Commented…
Question Number 53464 by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{U}_{{n}} =\:\frac{\left(\int_{\mathrm{0}} ^{{n}} \:{e}^{−{x}^{\mathrm{2}} } {dx}\right)^{\mathrm{2}} }{\int_{\mathrm{0}} ^{{n}} \:\:{e}^{−{nx}^{\mathrm{2}} } {dx}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{U}_{{n}}…
Question Number 53462 by maxmathsup by imad last updated on 22/Jan/19 $${find}\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{xsinx}}{{cos}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jan/19 $$\int{xtanxsecxdx}…
Question Number 118997 by Lordose last updated on 21/Oct/20 Answered by MJS_new last updated on 21/Oct/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{5}} }{dx}= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\right] \\ $$$$=−\frac{{x}\left(\mathrm{15}{x}^{\mathrm{6}} +\mathrm{110}{x}^{\mathrm{4}}…
Question Number 184523 by cortano1 last updated on 08/Jan/23 Answered by SEKRET last updated on 08/Jan/23 $$\:\:\:\boldsymbol{\mathrm{t}}=\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\:\:\:\:\:\boldsymbol{\mathrm{dt}}=\:−\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}\:\:\:\:\:\:\boldsymbol{\mathrm{dx}}=\:−\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\boldsymbol{\mathrm{dt}} \\ $$$$\:\:\int_{\infty} ^{\:\mathrm{1}} \frac{\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}^{\mathrm{5}} }}{\lfloor\boldsymbol{\mathrm{t}}\rfloor}\:\centerdot\left(\frac{−\mathrm{1}}{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\right)\boldsymbol{\mathrm{dt}}=\:\:\int_{\mathrm{1}}…