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Category: Integration

find-ln-x-x-1-dx-

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} \\…

find-x-1-x-1-x-1-x-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}…

let-f-x-0-pi-2-d-1-x-e-i-with-x-lt-1-1-developp-f-x-at-integr-serie-2-calculate-f-x-3-find-the-value-of-0-pi-2-e-i-1-x-e-i-2-4-calculate-0-pi-2

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}…

If-0-1-e-x-2-dx-a-then-find-the-value-of-0-1-x-2-e-x-2-dx-in-terms-of-a-

Question Number 38651 by rahul 19 last updated on 28/Jun/18 $$\mathrm{If}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:{a}\:,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}\:{in}\:{terms}\:{of}\:'{a}'\:? \\ $$ Answered…