I would like to see all the solutions for the following:

int(1/(a-(b+c)*t),t);

but the result only gives

(ln((-b-c)*t+a)/(-b-c)

For example, I can imagine that if b=-c in the integrand that the solution should be

t/a

and not undefined as it would be by substituting b=-c into the Maple result.

I tried

int(1/(a-(b+c)*x),x=0..t,AllSolutions);

but I didn't find that this gave the answer I was looking for either.