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Integral Help: Calculate cos^2(x) Integral
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[QUOTE="Ray Vickson, post: 4629771, member: 330118"] I am beginning to doubt there is a simple closed-form solution. However, one can reduce it to a finite integration that might be preferable to use if you want an accurate numerical value. Call the integral J, and note that we can re-write it as an integral over [0,∞): [tex] J = \int_0^{\infty} f(x) \, dx, \:\: f(x) = \frac{e^{-x}}{1 + \cos^2(2x)} [/tex] Since ##\cos^2(2x)## is periodic with period ##\pi/2## we have [tex] f\left( n \frac{\pi}{2} + t \right) = \alpha^n f(t), \; \alpha = e^{-\pi/2} [/tex] so [tex] J = \sum_{n=0}^{\infty} \alpha^n J_0 = \frac{J_0}{1-\alpha}, \text{ where } J_0 = \int_0^{\pi/2} f(x) \, dx. [/tex] For numerical work it might be better to work with J_0 instead of the original J. [/QUOTE]
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Integral Help: Calculate cos^2(x) Integral
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