1. ## Integration Confusion

I do not understand what method I can use to workout the following equation:

$
\int\frac{1}{e^{4x + 1}} dx
$

My first instinct was to say that $\frac{1}{4} ln e^{4x + 1}
$

However it is my understanding that ln e would cancel each other out. Thus the original equation would have only been 4x + 1, and the derivative of that is merely 4. So, I seem to be doing something wrong, what am I missing?

2. $\int \frac{1}{e^{4x+1}} \ dx = \int e^{-(4x+1)} \ dx$

Now let $u = -(4x+1)$