Question Number 169563 by cortano1 last updated on 03/May/22 Commented by infinityaction last updated on 03/May/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 169559 by TOTTI last updated on 03/May/22 Commented by cortano1 last updated on 03/May/22 $$\:\mathrm{2}^{{nd}} \:{way}\: \\ $$$$\:\:\begin{array}{|c|c|c|}{{x}}&\hline{\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\\{\mathrm{1}}&\hline{−\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\\{\mathrm{0}}&\hline{−\frac{\mathrm{4}}{\mathrm{15}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} }\\\hline\end{array} \\ $$$$\:{I}=\int\:{x}\:\sqrt{\mathrm{1}−{x}}\:{dx}\:=\:−\frac{\mathrm{2}}{\mathrm{3}}{x}\:\sqrt{\left(\mathrm{1}−{x}\right)^{\mathrm{3}}…
Question Number 169548 by mathlove last updated on 02/May/22 Commented by infinityaction last updated on 02/May/22 $$\int\frac{{x}}{\mathrm{2cos}\:^{\mathrm{2}} {x}/\mathrm{2}}{dx}\:+\:\int\frac{\mathrm{2sin}\:{x}/\mathrm{2}\:\mathrm{cos}\:{x}/\mathrm{2}}{\mathrm{2cos}\:^{\mathrm{2}} {x}/\mathrm{2}}{dx} \\ $$$$\underset{{by}\:{parts}\:} {\underbrace{\frac{\mathrm{1}}{\mathrm{2}}\int{x}\mathrm{sec}\:^{\mathrm{2}} {x}/\mathrm{2}\:{dx}}}\:+\:\int\mathrm{tan}\:{x}/\mathrm{2}\:{dx} \\ $$$${be}\:{continued}…
Question Number 38469 by maxmathsup by imad last updated on 25/Jun/18 $${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…
Question Number 38470 by maxmathsup by imad last updated on 25/Jun/18 $${calculate}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({tx}\right)}{\left(\mathrm{1}+{tx}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cosx}}{\left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 38468 by maxmathsup by imad last updated on 25/Jun/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right){sh}\left(\mathrm{3}{x}\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by math khazana by abdo last updated…
Question Number 38466 by maxmathsup by imad last updated on 25/Jun/18 $${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…
Question Number 38467 by maxmathsup by imad last updated on 25/Jun/18 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{cos}\left({ax}\right){ch}\left({bx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}\:. \\ $$ Commented by math khazana by abdo last updated…
Question Number 38465 by maxmathsup by imad last updated on 25/Jun/18 $${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{3}} \right){dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+\mathrm{4}{t}^{\mathrm{3}} \right){dt}\:\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{3}} \right){dt}. \\ $$…
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…