$\frac{1}{x^2+1} = \frac{1}{2i}\frac{Du}{u}$ with $u = \frac{1+ix}{1-ix}$ · Prove2Me

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$\frac{1}{x^2+1} = \frac{1}{2i}\frac{Du}{u}$ with $u = \frac{1+ix}{1-ix}$ · Prove2Me