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# Converting $\ln|x| = h$ to $x = e^h$

In Kreyszig’s Advanced Engineering Mathematics, section on First-Order ODEs, it is written:

$$dF/F = p \, dx$$

$$\ln|F| = h = \int p \, dx$$

Therefore, $$F = e^h$$

However I don’t understand why the absolute value for $$F$$ is gone.

To my understanding, a simplified version of this could be thought of as $$\ln|x| = h$$. Then if I write $$x = e^h = e^{\ln|x|}$$ just like the reasoning of the book, when I put $$x = -2$$, the equation would not hold true because $$e^{\ln|-2|} = e^{\ln2} = 2$$, not $$-2$$.