What is the integral of $e^x a^x$ Can you confirm that my answer below is correct?

$$\int (a^x e^x)dx $$

My attempt:

$$\int a^x e^x \, dx = \int (ae)^x \, dx $$ 
$$\int a^x e^x \, dx = \frac{(ae)^x}{\ln(ae)} + C $$
$$\int a^x e^x \, dx = \frac{a^xe^x}{\ln(ae)} + C $$
Yes, I can confirm that your answer above is correct.
Yes, I can confirm that your answer above is correct.