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Kostya_I
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I like to amuse calculus students with this trick: let us calculate by integrating by parts: $$ \int \frac{dx}{x}=\int (x')\frac{1}{x}\,dx=x\cdot\frac{1}{x}-\int x\cdot \left(\frac{1}{x}\right)'\,dx=1+\int\frac{dx}{x}, $$ and we simplify to $0=1$.

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