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Category: Integration

x-1-x-2-1-5-2-x-1-dx-

Question Number 93587 by  M±th+et+s last updated on 13/May/20 $$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}}{dx} \\ $$ Answered by niroj last updated on 13/May/20 $$\:\:\:\:\mathrm{I}=\:\int\:\frac{\:\:\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2x}−\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)+\:\frac{\mathrm{5}+\sqrt{\mathrm{5}}}{\mathrm{4}}}{\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\mathrm{x}+\mathrm{1}}\mathrm{dx}…

let-give-f-x-x-y-1-and-D-x-y-R-2-0-x-1-and-1-y-1-find-the-value-of-f-x-y-dxdy-

Question Number 28038 by abdo imad last updated on 19/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\sqrt{{x}+{y}}\:+\mathrm{1}\:\:{and}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\right. \\ $$$$\left.{and}\:−\mathrm{1}\leqslant{y}\leqslant\mathrm{1}\right\}\:\:{find}\:{the}\:{value}\:{of}\:\:\int\int\:{f}\left({x},{y}\right){dxdy}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-find-the-value-of-0-ln-x-1-x-2-dx-2-find-the-value-of-0-xln-x-1-x-2-2-dx-

Question Number 28033 by abdo imad last updated on 18/Jan/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo…

n-0-1-n-n-4-n-2-1-

Question Number 159080 by qaz last updated on 12/Nov/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$ Answered by mindispower last updated on 13/Nov/21 $$=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}!\left({n}^{\mathrm{2}}…