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}} \\ $$$$\:\:\int_{\infty} ^{\:\mathrm{1}} \frac{\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}^{\mathrm{5}} }}{\lfloor\boldsymbol{\mathrm{t}}\rfloor}\:\centerdot\left(\frac{−\mathrm{1}}{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\right)\boldsymbol{\mathrm{dt}}=\:\:\int_{\mathrm{1}}…
Question Number 184514 by BOYQOBILOV last updated on 08/Jan/23 Answered by SEKRET last updated on 19/Jan/23 $$\:\:\:\boldsymbol{\mathrm{t}}\:=\:\boldsymbol{\mathrm{x}}+\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:\:\:\:\:\:\:\:\:/_{\mathrm{0}} ^{\:\:\:\mathrm{1}} \rightarrow/_{\mathrm{1}} ^{\:\:\mathrm{1}+\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\boldsymbol{\mathrm{dt}}=\:\mathrm{1}+\frac{\boldsymbol{\mathrm{x}}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}\:\boldsymbol{\mathrm{dx}}=\:\frac{\boldsymbol{\mathrm{x}}+\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}}…
Question Number 118959 by bramlexs22 last updated on 21/Oct/20 $$\:\int\:\frac{{dx}}{{x}^{\mathrm{6}} −{x}^{\mathrm{3}} }\:? \\ $$ Answered by Dwaipayan Shikari last updated on 21/Oct/20 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}−\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} }…
Question Number 118955 by Bird last updated on 21/Oct/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnx}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Answered by mnjuly1970 last updated on 21/Oct/20 $$ \\ $$$${I}=\int_{\mathrm{0}}…
Question Number 53418 by Abdo msup. last updated on 21/Jan/19 $${find}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{x}}{\mathrm{2}+{cosx}\:{sinx}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…