$$\int \frac{1}{x}dx=\int1dx \frac{1}{x}-\int \left(\frac{d}{dx}\frac{1}{x}\int1dx\right)dx=1+\int\frac{1}{x}dx \Leftrightarrow 0=1$$
2026-03-27 12:17:40.1774613860
$0=1$, or I have done something wrong.
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yes! This is one of the integrals you should always remember! Recall that $$\frac{d}{dt}\left(\ln(x)\right)=\frac{1}{x}$$
hence $$\int \frac{1}{x} dx = \ln(|x|) + Constant$$