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Category: Integration

0-x-3-sin-x-x-4-4-dx-

Question Number 127468 by bramlexs22 last updated on 30/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{x}^{\mathrm{3}} \:\mathrm{sin}\:\left(\lambda\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\:\mathrm{dx}\:=?\: \\ $$ Commented by bramlexs22 last updated on 30/Dec/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:\mathrm{sir} \\…

let-A-x-1-x-2-x-1-x-2-2i-dx-1-calculate-A-2-extract-Re-A-and-Im-A-and-determine-its-values-i-2-1-

Question Number 61921 by maxmathsup by imad last updated on 11/Jun/19 $${let}\:{A}\:=\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} \:−\mathrm{2}{i}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{extract}\:{Re}\left({A}\right)\:{and}\:{Im}\left({A}\right)\:{and}\:{determine}\:{its}\:{values}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$ Commented by…

let-I-dx-x-i-n-and-J-dx-x-i-n-1-calculate-I-and-J-interms-of-n-2-find-thevalue-of-integral-A-n-cos-narctan-1-x-1-x-2-n-

Question Number 61885 by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}+{i}\right)^{{n}} }\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}−{i}\right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:{and}\:{J}\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{thevalue}\:{of}\:{integral} \\ $$$${A}_{{n}} \:\:=\int_{−\infty}…

let-f-n-a-cos-nx-x-2-x-a-2-dx-with-a-1-1-find-a-explicit-form-of-f-n-a-2-study-the-convervenge-of-f-n-a-3-determine-also-g-n-a-cos-nx

Question Number 61884 by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{f}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} +{x}\:\:+{a}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\:\:{a}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convervenge}\:{of}\:\Sigma\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{also}\:{g}_{{n}}…

xln-x-x-ln-3-x-dx-

Question Number 61874 by aliesam last updated on 10/Jun/19 $$\int\frac{{xln}\left({x}\right)−{x}}{{ln}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$ Commented by Prithwish sen last updated on 10/Jun/19 $$\int\left[\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{2}} }\:−\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} }\:\right]\mathrm{dx} \\…