If $I = \int \frac{\sin x + \sin^3 x}{\cos 2x}\,dx = P \cos x + Q \log \left| \frac{\sqrt{2}\cos x - 1}{\sqrt{2}\cos x + 1} \right| + C$, then the values of $P$ and $Q$ are respectively:
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For integrals with mixed trigonometric powers, the substitution $u = \cos x$ often converts the integrand into a rational function that is easier to handle.