Question

\[-\int e^{t} dt = -e^{t}\]
\[ln(-e^{t}) = -t?\]

Answer 1

Over the real numbers
\[\ln(-e^t)\]
doesn't make any sense. Over the complex numbers however, this is given by:
\[e^{i \pi} = -1 \implies \ln(-e^t)=\ln(e^{i \pi}e^t)=\ln(e^{i \pi})+\ln(e^t)=i \pi + t\]

Answer 2

I.e, when dealing with real numbers you can't put negatives into logarithms.

Answer 3

thanks

Answer 4

@malevolence19 can you take a look at a new question that I have posted? That's where this question originated from