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Category: Integration

decompose-F-x-x-2-x-4-1-imside-R-x-2-find-the-value-of-2-x-2-x-4-1-

Question Number 33334 by prof Abdo imad last updated on 14/Apr/18 $${decompose}\:{F}\left({x}\right)=\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:−\mathrm{1}}\:{imside}\:{R}\left({x}\right)\: \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{2}} ^{+\infty} \:\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:−\mathrm{1}}\:\:. \\ $$ Commented by prof…

let-consider-the-2pi-periodic-function-f-x-e-x-1-developp-f-at-fourier-serie-2-find-the-value-of-n-0-1-n-n-2-1-

Question Number 33310 by abdo imad last updated on 14/Apr/18 $${let}\:{consider}\:{the}\:\mathrm{2}\pi\:{periodic}?{function}\:\:{f}\left({x}\right)\:={e}^{{x}} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Terms of Service Privacy…

find-0-pi-2-ln-1-x-sin-d-with-0-lt-x-lt-1-2-calculate-0-pi-2-ln-1-1-2-sin-d-

Question Number 33297 by abdo imad last updated on 14/Apr/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}+{x}\:{sin}\theta\right){d}\theta\:\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}\theta\right){d}\theta \\ $$ Terms of Service Privacy Policy Contact:…

Question-98831

Question Number 98831 by bramlex last updated on 16/Jun/20 Commented by john santu last updated on 16/Jun/20 $$\int\:\frac{\mathrm{2}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{8}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)}\:=\:\int\:\frac{\mathrm{2d}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)}{\mathrm{7}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{7}} }\right)} \\ $$$$=\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{7}} −\mathrm{1}}{\mathrm{x}^{\mathrm{7}}…