About the function $ f(a) = \int \limits_0^{\infty} \frac{\ln y}{e^{ay} + 1} \ dy $

About the function $ f(a) = \int \limits_0^{\infty} \frac{\ln y}{e^{ay} +
1} \ dy $

We define the following function $$ f(a) = \int_0^{\infty} \frac{\ln
y}{e^{ay} + 1} \ dy $$
and $$ f(r) = f'(r') = 0 $$ find $$ \int_r^{r'} f(a) \ da $$