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**Integral of 1/x = ln(x)... Problem has missing absolute value!?**

This is an ODE problem and solution, but what I'm not understanding here is calculus based:

Why does the argument to the red-boxed ln() not in absolute value signs?? ( | | )

u = cos(t) so the numerator can be negative. I am just confused as to why they left that out.

Thanks for any help.

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