Is 0=1? Then find the mistake

Consider the integral, $\displaystyle I =\int \dfrac{1}{x}dx$

We know that $I= \log x$

But, $\displaystyle I =\int \dfrac{1}{x}(1)dx =(x)\dfrac{1}{x}-\int \bigg(-\dfrac{1}{x^2} \bigg) xdx$

$1+I=I \Rightarrow 1=0$

What is the mistake?

I do not know the mistake

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