Integration - Integrable Forms of Trigonometric Functions

Integration - Integrable Forms of Trigonometric Functions

Junior College 2

\[\int \frac{1}{\sin^3x+\cos^3x} \, \mathrm{d}x\]

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Answer:\[ \frac{\sqrt{2}}{6} \ln \left| \frac{\cos x - \sin x - \sqrt{2}}{\cos x - \sin x + \sqrt{2}} \right| - \frac{2}{3} \tan^{-1} (\cos x - \sin x) + C \]

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