I m doing this interal with Mathematica
what I get back is
1/(1 + b t) + Log[-b t] - Log[1 + b t]
However there is a problem with the second term: imagine I set b to some positive number, as well as t, this would lead to an imaginary number instead a real one, as should be for a real integral. Indeed, just changing the sign works good, but I am puzzled about why Mathematica choses this solution. I guess must be related to choosing some branch for the logarithm or something similar, but still I don't figure out what Any suggestions?