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Question Number 33507 by MJS last updated on 18/Apr/18

∫((2cos x)/(3−cos 2x))dx=?

$$\int\frac{\mathrm{2cos}\:{x}}{\mathrm{3}−\mathrm{cos}\:\mathrm{2}{x}}{dx}=? \\ $$

Answered by math1967 last updated on 18/Apr/18

∫((2cosx)/(3−1+2sin^2 x))dx  ∫((2cosx)/(2(1+sin^2 x)))dx  ∫((d(sinx))/(1+sin^2 x))  tan^(−1) sinx +c

$$\int\frac{\mathrm{2}{cosx}}{\mathrm{3}−\mathrm{1}+\mathrm{2}{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\int\frac{\mathrm{2}{cosx}}{\mathrm{2}\left(\mathrm{1}+{sin}^{\mathrm{2}} {x}\right)}{dx} \\ $$$$\int\frac{{d}\left({sinx}\right)}{\mathrm{1}+{sin}^{\mathrm{2}} {x}} \\ $$$$\mathrm{tan}^{−\mathrm{1}} {sinx}\:+{c} \\ $$

Commented by MJS last updated on 18/Apr/18

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

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