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Use the reduction formula ∫cos⁡nx dx=1ncos⁡n−1xsin⁡x+n−1n∫cos⁡n−2x dx\int\cos^n x\,dx = \frac1n\cos^{n-1}x\sin x + \frac{n-1}{n}\int\cos^{n-2}x\,dx to compute ∫cos⁡4x dx\int\cos^{4} x\,dx.
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