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Category: Integration

calculate-f-a-sin-ax-x-2-x-1-dx-2-find-the-value-of-sin-3x-x-2-x-1-dx-

Question Number 38469 by maxmathsup by imad last updated on 25/Jun/18 $${calculate}\:\:{f}\left({a}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({ax}\right)}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}{dx} \\ $$ Commented by math…

calculate-f-t-0-cos-tx-1-tx-2-2-dx-with-t-0-2-find-the-values-of-0-cos-2x-1-2x-2-2-dx-and-0-cosx-2-x-2-2-dx-

Question Number 38470 by maxmathsup by imad last updated on 25/Jun/18 $${calculate}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({tx}\right)}{\left(\mathrm{1}+{tx}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cosx}}{\left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{2}}…

let-a-from-R-find-F-a-t-cos-tx-a-2-x-2-dx-2-calculate-F-2-3-and-F-3-2-

Question Number 38466 by maxmathsup by imad last updated on 25/Jun/18 $${let}\:{a}\:{from}\:{R}\:\:{find}\:{F}_{{a}} \left({t}\right)=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({tx}\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{F}_{\mathrm{2}} \left(\mathrm{3}\right)\:\:{and}\:{F}_{\mathrm{3}} \left(\mathrm{2}\right) \\ $$ Commented by…

find-f-x-0-1-ln-1-xt-3-dt-with-x-lt-1-2-calculate-0-1-ln-1-4t-3-dt-and-0-1-ln-2-t-3-dt-

Question Number 38465 by maxmathsup by imad last updated on 25/Jun/18 $${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{3}} \right){dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+\mathrm{4}{t}^{\mathrm{3}} \right){dt}\:\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{3}} \right){dt}. \\ $$…

let-f-x-0-1-ln-1-x-2-t-2-t-2-dt-with-x-lt-1-find-f-x-at-a-simple-form-

Question Number 38464 by maxmathsup by imad last updated on 25/Jun/18 $${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:\:{f}\left({x}\right)\:{at}\:{a}\:{simple}\:{form}\:. \\ $$ Commented by abdo.msup.com last…

find-f-x-0-arctan-1-e-xt-dt-with-x-gt-0-2-find-0-arctan-1-e-2t-dt-

Question Number 38461 by maxmathsup by imad last updated on 25/Jun/18 $${find}\:\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:{arctan}\left(\mathrm{1}+{e}^{−{xt}} \right){dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:\:{arctan}\left(\mathrm{1}+{e}^{−\mathrm{2}{t}} \right){dt}. \\ $$ Terms of Service…