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Category: Integration

let-I-n-x-0-t-sin-t-t-2-x-2-n-dt-1-find-a-relation-between-I-n-1-and-I-n-2-calculate-I-2-x-and-I-3-x-3-calculate-0-tsin-t-2-t-2-2-dt-

Question Number 36187 by prof Abdo imad last updated on 30/May/18 $${let}\:{I}_{{n}} \left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{sin}\left({t}\right)}{\left({t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{{n}} }{dt}\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{1}} \:\:{and}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{2}} \left({x}\right)\:{and}\:{I}_{\mathrm{3}} \left({x}\right)\:…

let-give-I-0-dx-x-2-i-2-1-extract-Re-I-and-Im-I-2-find-the-value-of-I-3-calculate-Re-I-and-Im-I-

Question Number 36167 by abdo mathsup 649 cc last updated on 29/May/18 $${let}\:{give}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{i}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{extract}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{Re}\left({I}\right)\:{and}\:{Im}\left({I}\right)\:. \\ $$…

sin-3-3x-cos-4-5x-dx-

Question Number 167223 by cortano1 last updated on 10/Mar/22 $$\:\:\int\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3x}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{5x}\right)\:\mathrm{dx}=? \\ $$ Commented by greogoury55 last updated on 10/Mar/22 $$\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3}{x}\right)=\frac{\mathrm{3sin}\:\left(\mathrm{3}{x}\right)−\mathrm{sin}\:\left(\mathrm{9}{x}\right)}{\mathrm{4}} \\ $$$$\:\mathrm{cos}\:^{\mathrm{4}}…