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

[JJHK]

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

Hi, I know that:

∫a^x dx = a^x / ln(a) + C

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

 

[DivisionByZro]

Here's a trick:

Re-write your integral as:

$$<br /> \int e^{lna*x}dx$$

Then use a substitution:

u = ln(a) * x

 

[JJHK]

Beautiful! Thank you :D