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

[Jonnyb42]

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.

 

[Jonnyb42]

My solution is that, it is an Initial value problem, (there is only one t which we care about) and with that t the argument in the natural log is positive and so u can ignore the abs value!