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∫0π/3∑n=1∞[sin(x)sin(x+πn)sin(x+2πn)⋯sin(x+(n−1)πn)] dx=lna\displaystyle \int_0^{\pi/3} {\sum_{n=1}^{\infty}{\left[\sin(x) \sin\left(x + \frac{\pi}{n}\right) \sin\left(x + \frac{2\pi}{n}\right) \cdots \sin\left(x + \frac{(n-1)\pi}{n}\right)\right]}\, dx} = \ln a∫0π/3n=1∑∞[sin(x)sin(x+nπ)sin(x+n2π)⋯sin(x+n(n−1)π)]dx=lna
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