On Tuesday, April 26, 2016 at 7:41:44 AM UTC-7, Laurent Decreusefond wrote:
>
>
> What does mean log(-1+e^(-2*t)) since the argument is negative ?
>

For t<0 that expression takes real values, so there the answer even makes 
sense in a real setting. The answer is generally correct for complex values 
t. You have to be careful that log is a multi-valued function, though, so 
if you want to use this antiderivative to compute definite integrals, you 
have to take care that appropriate branches are chosen. Luckily, for t>0 
the branch choice seems consistent, so:

sage: I=integrate(exp(-2*t)/(1-exp(-2*t)),t)
sage: (I(t=2)-I(t=1)).n()
0.0634640055214862

looks like a reasonable answer.


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