Question Number 38728 by maxmathsup by imad last updated on 28/Jun/18 $${find}\:{L}\:\left(\:\frac{{e}^{−\frac{{x}}{{a}}} }{{a}}\right)\:\:{with}\:{a}\neq\mathrm{0}\:\:{and}\:{L}\:{laplace}\:{transfom}. \\ $$ Commented by abdo mathsup 649 cc last updated on 29/Jun/18…
Question Number 38727 by maxmathsup by imad last updated on 28/Jun/18 $${let}\:{n}\:{from}\:{N}\:\:{and}\:\:{A}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx}\:\:{and} \\ $$$${B}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx} \\…
Question Number 38724 by maxmathsup by imad last updated on 28/Jun/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} {cos}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 38719 by maxmathsup by imad last updated on 28/Jun/18 $${find}\:\:\:\int\:\:{ln}\left(\sqrt{{x}}\:+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Answered by behi83417@gmail.com last updated on 29/Jun/18 $${I}={xln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right)−\int{x}\frac{\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}+\mathrm{1}}}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}}{dx}= \\ $$$$={do}−\int\frac{{x}}{\mathrm{2}\sqrt{{x}}\sqrt{{x}+\mathrm{1}}}{dx}={do}−\int\frac{\sqrt{{x}}}{\mathrm{2}\sqrt{{x}+\mathrm{1}}}{dx} \\…
Question Number 38720 by maxmathsup by imad last updated on 28/Jun/18 $${find}\:\:\:\int\:\:\:\:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{dx} \\ $$ Commented by math khazana by abdo last updated on 28/Jun/18 $${the}\:{Q}\:{is}\:{find}\:\:\int\:\:\:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}−\mathrm{1}}}{dx}…
Question Number 38718 by maxmathsup by imad last updated on 28/Jun/18 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}+{x}\:{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}\:\:+{cos}\theta\right){d}\theta \\ $$$$ \\ $$ Commented by math…
Question Number 38716 by maxmathsup by imad last updated on 28/Jun/18 $${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\:\frac{{dx}}{\left({x}\:+\mathrm{1}−\left[{x}\right]\right)^{\mathrm{2}} } \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 38714 by maxmathsup by imad last updated on 28/Jun/18 $${calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{6}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{1}+{x}^{\mathrm{2}} \left[{x}\right]}{dx} \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 38706 by abdo mathsup 649 cc last updated on 28/Jun/18 $${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{d}\theta}{\mathrm{1}+{x}\:{e}^{{i}\theta} }\:\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{e}^{{i}\theta} }{\left(\mathrm{1}+{x}\:{e}^{{i}\theta}…
Question Number 104220 by bemath last updated on 20/Jul/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}^{\mathrm{2}} \mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx}\:?\: \\ $$ Commented by bemath last updated on 20/Jul/20 $${thank}\:{you}\:{both}.\:{cooll} \\…