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Category: Integration

find-x-1-cosx-dx-

Question Number 43914 by maxmathsup by imad last updated on 17/Sep/18 $${find}\:\int\:\:\:\:\frac{{x}}{\:\sqrt{\mathrm{1}+{cosx}}}{dx}\:. \\ $$ Commented by maxmathsup by imad last updated on 19/Sep/18 $${let}\:{A}\:=\:\int\:\:\:\:\:\frac{{x}}{\:\sqrt{\mathrm{1}+{cosx}}}{dx}\:{we}\:{have}\:{A}\:=\:\int\:\:\:\frac{{x}}{\:\sqrt{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}}{dx}…

find-f-a-t-0-2pi-dx-a-t-sinx-2-calculate-0-2pi-sinx-a-tsinx-2-dx-3-calculate-0-2pi-dx-a-tsinx-2-

Question Number 43909 by abdo.msup.com last updated on 17/Sep/18 $${find}\:{f}\left({a},{t}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{a}\:+{t}\:{sinx}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sinx}}{\left({a}+{tsinx}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{\left({a}+{tsinx}\right)^{\mathrm{2}} }\:. \\ $$ Answered…

x-sin-x-1-cos-x-dx-

Question Number 174965 by cortano1 last updated on 15/Aug/22 $$\:\:\:\:\:\:\int\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by som(math1967) last updated on 15/Aug/22 $$\int\frac{{x}}{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx}+\int\frac{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}}{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int{xsec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}{dx}\:+\int{tan}\frac{{x}}{\mathrm{2}}{dx}…

sin-3-x-dx-

Question Number 43861 by Tinkutara last updated on 16/Sep/18 $$\int\mathrm{sin}^{\mathrm{3}} \:\sqrt{{x}}\:{dx} \\ $$ Commented by Tinkutara last updated on 16/Sep/18 $${Answer}\:{given}\:{is} \\ $$$$−\mathrm{3}{x}^{\mathrm{3}/\mathrm{2}} \mathrm{cos}^{\mathrm{3}} \:\sqrt{{x}}\:+\mathrm{6}{x}^{\mathrm{1}/\mathrm{3}}…