# Thread: more integration by parts

1. ## more integration by parts

Is there some property of ln for the underlined part? i dont get how they got the anti derivative

2. $\frac{d}{dx}a^x = \ln(a)a^x$

So you want to find the function, which derivative gives you $a^x$ and that function is thus given by:

$\frac{d}{dx} \frac{a^x}{\ln(a)} = \frac{1}{\ln(a)} \frac{d}{dx} a^x = \frac{\ln(a)}{\ln(a)} a^x = a^x.$

3. cool, thanks again