Question Number 39037 by maxmathsup by imad last updated on 01/Jul/18 $$\:{calculate}\:\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{4}{t}\right)}{{x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cost}\:+\mathrm{1}}\:{dt} \\ $$ Commented by math khazana by abdo last updated…
Question Number 39034 by maxmathsup by imad last updated on 01/Jul/18 $${calculate}\:{interms}\:{of}\:{n} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left({nx}\right)}{{cosx}\:+{sinx}}{dx}\:\:{and}\:{B}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sin}\left({nx}\right)}{{cosx}\:+{sinx}}{dx}\:. \\ $$ Commented by math…
Question Number 39035 by maxmathsup by imad last updated on 01/Jul/18 $${find}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:{sin}\left({x}\right){e}^{−{t}\:\left[{x}\right]} {dx}\:\:\:{with}\:{t}>\mathrm{0} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 39033 by maxmathsup by imad last updated on 01/Jul/18 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{xsin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by math khazana by abdo last…
Question Number 39029 by MJS last updated on 01/Jul/18 $$\int\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}{dx}=? \\ $$$$\int\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}}{dx}=? \\ $$ Answered by MJS last updated on 02/Jul/18 $$\int\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=−\mathrm{3}+\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}\:\rightarrow\:{dx}=\frac{\mathrm{2}}{\mathrm{5}}{x}^{\mathrm{2}} \sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}{dt}\right]…
Question Number 39030 by maxmathsup by imad last updated on 01/Jul/18 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} }\:\:{with}\:{x}\:>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}}…
Question Number 39025 by maxmathsup by imad last updated on 01/Jul/18 $${let}\:{f}\left({x}\right)=\:\frac{{cos}\left(\alpha{x}\right)}{{cosx}}\:\:\:\:\left(\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$ Commented by math khazana by abdo last updated on…
Question Number 39023 by maxmathsup by imad last updated on 01/Jul/18 $${let}\:{g}\left({x}\right)=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{arctan}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{g}\left({x}\right)\:. \\ $$ Commented by math khazana by…
Question Number 39024 by maxmathsup by imad last updated on 01/Jul/18 $${find}\:{the}\:{value}\:{of}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}\:{dx} \\ $$ Commented by math khazana by abdo last updated…
Question Number 39019 by maxmathsup by imad last updated on 01/Jul/18 $${calculate}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$ Commented…