Category: Integration

Question Number 37884 by prof Abdo imad last updated on 18/Jun/18 $${let}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{x}\right]} \:{cos}^{\mathrm{2}} \left(\mathrm{2}\pi{x}\right){dx}\:{and}\: \\ $$$${J}\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]} \:{sin}^{\mathrm{2}} \left(\mathrm{2}\pi{x}\right)\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:{and}\:{I}\:−{J} \\…

Question Number 168894 by mnjuly1970 last updated on 20/Apr/22 Commented by mahdipoor last updated on 20/Apr/22 $$\int\frac{\mathrm{1}}{\mathrm{12}}\left(\frac{\mathrm{3}−{x}}{{x}^{\mathrm{2}} +{x}}+\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\right){dx}= \\ $$$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}=\int\frac{{d}\left({lnx}\right)}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}= \\…

Question Number 37820 by prof Abdo imad last updated on 17/Jun/18 $${let}\:{f}\left({x}\right)=\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 37812 by prof Abdo imad last updated on 17/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{x}} {sin}\left\{\pi\left[{x}\right]\right\}{dx}\:. \\ $$ Commented by abdo mathsup 649 cc last updated…

Question Number 103343 by Dwaipayan Shikari last updated on 14/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$ Answered by mathmax by abdo last updated on 15/Jul/20…