Question Number 36422 by abdo.msup.com last updated on 01/Jun/18 $${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \left({t}^{\mathrm{2}} +\mathrm{1}\right){arctan}\left({t}\right){dt}\:. \\ $$ Commented by prof Abdo imad last updated on 04/Jun/18 $${let}\:{integrate}\:{by}\:{parts}\:{u}^{'}…
Question Number 101959 by MathQoutes last updated on 05/Jul/20 $$ \\ $$$$ \\ $$$${Starting}\:{from} \\ $$$$\:\:\:\:\:\:\:\:{y}=\frac{\mathrm{4}}{\:\sqrt{\pi}}{t}^{\frac{\mathrm{3}}{\mathrm{2}}\:} \int_{\mathrm{0}} ^{\infty} {x}^{\mathrm{3}} {e}^{−{tx}^{\mathrm{2}} } {dx} \\ $$$${find}\:\:\:\frac{\pi}{\mathrm{8}}=? \\…
Question Number 36420 by abdo.msup.com last updated on 01/Jun/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\:{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy…
Question Number 36421 by abdo.msup.com last updated on 01/Jun/18 $${find}\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}−{x}}} \\ $$ Commented by abdo.msup.com last updated on 04/Jun/18 $${changement}\:\sqrt{\mathrm{1}−{x}}={t}\:{give}\:\mathrm{1}−{x}={t}^{\mathrm{2}} \\ $$$${I}\:=\:\int\:\:\:\:\:\frac{−\mathrm{2}{tdt}}{\mathrm{1}+\mathrm{2}{t}}\:=\:−\int\:\frac{\mathrm{2}{t}+\mathrm{1}−\mathrm{1}}{\mathrm{2}{t}\:+\mathrm{1}}{dt} \\ $$$$=−{t}\:+\:\int\:\:\:\:\frac{{dt}}{\mathrm{2}{t}\:+\mathrm{1}}\:=\:−{t}\:\:+\frac{\mathrm{1}}{\mathrm{2}}{ln}\mid\mathrm{2}{t}+\mathrm{1}\mid\:+{c} \\…
Question Number 36419 by abdo.msup.com last updated on 01/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by abdo.msup.com last updated on 04/Jun/18 $${we}\:{have}\:{I}\:=\:\int_{\mathrm{0}}…
Question Number 36417 by abdo.msup.com last updated on 01/Jun/18 $${calculate}\:\int_{\mathrm{2}} ^{\mathrm{6}} \:\:\:\frac{{dx}}{\:\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}−\mathrm{1}}} \\ $$ Commented by abdo mathsup 649 cc last updated on 03/Jun/18 $${I}\:=\:\int_{\mathrm{2}}…
Question Number 36418 by abdo.msup.com last updated on 01/Jun/18 $${calculate}\:\:\int_{−\mathrm{3}} ^{\mathrm{4}} \mid{x}^{\mathrm{2}} \:−\mathrm{2}{x}−\mathrm{3}\mid{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 $${x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3} \\…
Question Number 36416 by abdo.msup.com last updated on 01/Jun/18 $${calculate}\:{I}\:=\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\frac{\mathrm{2}{x}^{\mathrm{3}} \:+\mathrm{5}{x}^{\mathrm{2}} \:−\mathrm{4}{x}−\mathrm{7}}{\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 36415 by abdo.msup.com last updated on 01/Jun/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({x}^{\mathrm{3}} \:+{x}\right){cos}^{\mathrm{2}} {xdx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\left({x}^{\mathrm{3}} \:+{x}\right){sin}^{\mathrm{2}} {xdx} \\ $$$${cslculate}\:{I}\:{and}\:{J}\:. \\ $$ Commented…
Question Number 36413 by abdo.msup.com last updated on 01/Jun/18 $${let}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{3}+{x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} {I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{I}_{{n}} \\ $$ Commented by abdo.msup.com…