Question Number 127885 by psyche last updated on 02/Jan/21 $$\int\left(\frac{\mathrm{sin}\:\left(\mathrm{2tan}^{−\mathrm{1}} \left({x}\right)+{x}\right)}{{x}}\right)\:\:{the}\:{limit}\:\left[\mathrm{0},\infty\right) \\ $$ Answered by Lordose last updated on 02/Jan/21 $$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{2tan}^{−\mathrm{1}}…
Question Number 62343 by maxmathsup by imad last updated on 20/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left\{{x}\prod_{{k}=\mathrm{1}} ^{\infty} \:{cos}\left(\frac{{x}}{\mathrm{2}^{{k}} }\right)\right\}{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 62342 by maxmathsup by imad last updated on 20/Jun/19 $${let}\:{f}\left(\xi\right)\:=\int\:\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}{dx}\:\:\:{with}\:\:\mathrm{0}<\xi<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{\xi\rightarrow\mathrm{1}} \:\:\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} \theta\:{x}^{\mathrm{2}}…
Question Number 127870 by Eric002 last updated on 02/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2021} \\ $$$${HAPPY}\:{NEW}\:{Year} \\ $$$$\left.\mathrm{1}\right)\int\frac{{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{1}\right)}{dx} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\int\frac{\mathrm{2}{cos}\left({x}\right)−{sin}\left({x}\right)}{\mathrm{3}{sin}\left({x}\right)+\mathrm{5}{cos}\left({x}\right)}{dx} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\int\frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{6}}…
Question Number 62335 by maxmathsup by imad last updated on 19/Jun/19 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{xt}} {cos}\left({yt}\right)}{\:\sqrt{{t}}}\:{dt}\:{and}\:{g}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{xt}} {sin}\left({yt}\right)}{\:\sqrt{{t}}}\:{dt} \\ $$$${with}\:{x}>\mathrm{0}\:\:{and}\:{y}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−\mathrm{2}{t}} \:{cos}\left({t}\right)}{\:\sqrt{{t}}}\:{dt}\:{and}\:\int_{\mathrm{0}}…
Question Number 62330 by maxmathsup by imad last updated on 19/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt}\:\:\:{with}\:\:\:\mathrm{0}<{a}<\mathrm{1} \\ $$ Commented by mathmax by abdo last updated…
Question Number 127857 by slahadjb last updated on 02/Jan/21 $$\int\sqrt{{x}}{e}^{{x}} {dx}\:\:? \\ $$ Commented by Dwaipayan Shikari last updated on 02/Jan/21 $$\int{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}}…
Question Number 127851 by bemath last updated on 02/Jan/21 $$\:\psi\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\sqrt[{\mathrm{5}}]{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{1}\right)^{\mathrm{3}} }}\:?\: \\ $$ Answered by liberty last updated on 02/Jan/21 $$\:\psi\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\sqrt[{\mathrm{5}}]{\mathrm{x}^{\mathrm{15}} \left(\mathrm{1}+\mathrm{x}^{−\mathrm{5}}…
Question Number 127833 by Algoritm last updated on 02/Jan/21 Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{4}} \:\frac{\mathrm{cosx}}{\:\sqrt{\mathrm{4}−\mathrm{x}}}\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\sqrt{\mathrm{4}−\mathrm{x}}=\mathrm{t}\:\Rightarrow\mathrm{4}−\mathrm{x}=\mathrm{t}^{\mathrm{2}} \\ $$$$\mathrm{I}\:=\int_{\mathrm{2}} ^{\mathrm{0}} \:\frac{\mathrm{cos}\left(\mathrm{4}−\mathrm{t}^{\mathrm{2}}…
Question Number 127815 by Algoritm last updated on 02/Jan/21 Commented by Algoritm last updated on 02/Jan/21 $$\mathrm{prove}\:\mathrm{the}\:\mathrm{equation} \\ $$ Terms of Service Privacy Policy Contact:…