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Category: Integration

calculate-interms-of-n-A-n-0-2pi-cos-nx-cosx-sinx-dx-and-B-n-0-2pi-sin-nx-cosx-sinx-dx-

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…

3-5-1-1-x-1-3-dx-1-3-5-1-1-x-1-3-dx-

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]…

1-let-f-x-0-dt-1-x-2-t-4-with-x-gt-0-find-a-simple-form-of-f-x-2-calculate-0-dt-1-t-4-3-calculate-0-dt-1-3t-4-

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}}…