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Category: Integration

cosx-2-cosx-dx-

Question Number 27614 by NECx last updated on 10/Jan/18 $$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx} \\ $$ Commented by abdo imad last updated on 11/Jan/18 $$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx}=\:−\int\frac{\mathrm{2}−{cosx}\:+\mathrm{2}}{\mathrm{2}−{cosx}}{dx}\:=\:−{x}\:+\mathrm{2}\int\:\frac{{dx}}{\mathrm{2}−{cox}}\:\:{but} \\ $$$${the}\:{ch}.\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}\: \\ $$$$\int\frac{{dx}}{\mathrm{2}−{cosx}}=\:\int\:\frac{\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…

1-3-cos-2-x-dx-

Question Number 27612 by NECx last updated on 10/Jan/18 $$\int\frac{\mathrm{1}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by ajfour last updated on 11/Jan/18 $$=\int\frac{\mathrm{sec}\:^{\mathrm{2}} {xdx}}{\mathrm{3sec}\:^{\mathrm{2}} {x}+\mathrm{1}}=\int\frac{{d}\left(\mathrm{tan}\:{x}\right)}{\mathrm{4}+\mathrm{3tan}\:^{\mathrm{2}} {x}} \\…

1-2sin-2-x-4cos-2-x-dx-

Question Number 27611 by NECx last updated on 10/Jan/18 $$\int\frac{\mathrm{1}}{\mathrm{2sin}\:^{\mathrm{2}} {x}\:+\:\mathrm{4cos}\:^{\mathrm{2}} {x}}{dx} \\ $$ Answered by ajfour last updated on 11/Jan/18 $$=\int\frac{\mathrm{sec}\:^{\mathrm{2}} {xdx}}{\mathrm{2tan}\:^{\mathrm{2}} {x}+\mathrm{4}}=\int\frac{{dt}}{\mathrm{2}{t}^{\mathrm{2}} +\mathrm{4}}\:\:;\left({t}=\mathrm{tan}\:{x}\right)…