How to integrate a/1-ay?

In private correspondence with the author of the question, it was determined
that 'y' is the variable of integration.

Therefore, 'a' is a constant for purposes of this integration, and that whole
'a' business can be taken outside the integral.

Integral [a/(1-ay) dy] = a/(1-a) integral [dy/y] = a ln(y)/(1-a)    +  C