I have seen all sorts of things follow the $d$ in integrals, including $dy$, $dx$, and $d^2x$. Does just about anything go? Can I follow the $d$ with an expression, as in $∫ (4x + 17)$$d(4x + 17)$?
2026-04-02 20:05:30.1775160330
What can correctly follow the $d$ in an integral?
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Given $y$ is some well behaved function of $x$, then $dy=\frac{dy}{dx}dx$. So as long as your function $y$ that you put there is differentiable on the range of the integral, what $y$ is doesn't matter. If $y=4x+17$, then as mentioned in a comment, $dy=d(4x+17)=\frac{d(4x+17)}{dx}dx=4dx$.
$y=4x+17$ is differentiable on the full set of reals so you need to have no worries about this, if your function $y$ has singularities at $0$ or some other value, or some other non-differentiable points, you must be more careful.