What is the integral of $e^x a^x$

Question

Can you confirm that my answer below is correct?

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

My attempt:

$$\int a^x e^x \, dx = \int (ae)^x \, dx $$ $$\int a^x e^x \, dx = \frac{(ae)^x}{\ln(ae)} + C $$ $$\int a^x e^x \, dx = \frac{a^xe^x}{\ln(ae)} + C $$

Answer 1

Yes, I can confirm that your answer above is correct.