Average value of function that converges?

Question

I have a function $f$ that converges to a value:

$$ f(x) = 1−s−A \beta ^ x $$ Where $A \in \mathcal{R}$, and $0< \beta <1 $, $0< A <1 $

I want to get the average value of for $ x > r$. Since $ \beta $ is a number between 0 and 1, I know the function converges. But I don't know how to calculate the integral :(

I would imagine it has something to do with: $$ \int_r ^\infty 1−s− A \cdot \beta ^ x \partial x $$

But I have no clue on how to calculate this.

Any help?

Answer 1

Hint: $$\int a^x\,dx=\frac1{\ln a}a^x+C$$ What can you say about the convergence?