# Thread: Integrating a^x wrt x

1. ## Integrating a^x wrt x

I have $y=7^x$ and originally I wanted to derive this, but now I want to integrate it. How do I find $\int 7^x dx$?

2. Originally Posted by emterics90
I have $y=7^x$ and originally I wanted to derive this, but now I want to integrate it. How do I find $\int 7^x dx$?
$\int a^x~dx = \frac {1}{\ln a} a^x + C$

3. $\int7^x\,dx=\int e^{x\ln7}\,dx$

Let's set $u=x\ln7\implies du=\ln7\,dx$, this yields

$\int7^x\,dx=\frac1{\ln7}\int e^u\,du=\frac1{\ln7}e^{x\ln7}+k=\frac{7^x}{\ln7}+k ,\,k\in\mathbb R$