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$\displaystyle\lim_{R \rightarrow \infty} R \displaystyle\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{it} \log\left( 1 + \dfrac{1}{Re^{it}} \right) \mathrm{d}t = \pi$
The Houston Problem Book (wiki)
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Differential analyzer
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