I am currently learning how to find antiderivatives using the "$u$-substitution" or "integration by substitution" method. A key component of this is setting some expression in the indefinite integral as "$u$", and then also finding $du/dx$.
How can we then write $du = dx \cdot $ (some expression)? Isn't $du/dx$ defined as the derivative of $u$ and is not a fraction?
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