# Proving that the integral of (a^x)dx = a^x/(lna)+c ?

1. Feb 17, 2012

### JJHK

Proving that the integral of (a^x)dx = a^x/(lna)+c ???

Hi, I know that:

∫ax dx = ax / ln(a) + C

Could someone give me a step by step that proves this? thanks a lot!

2. Feb 17, 2012

### DivisionByZro

Re: Proving that the integral of (a^x)dx = a^x/(lna)+c ???

Here's a trick:

$$\int e^{lna*x}dx$$

Then use a substitution:

u = ln(a) * x

3. Feb 17, 2012

### JJHK

Re: Proving that the integral of (a^x)dx = a^x/(lna)+c ???

Beautiful! Thank you :D