# Simple integral

1. May 9, 2005

### Chaz706

My brain is truly fried.

I know this:
$$\int e^u du = e^u +C$$

But what do I do if I get this:
$$\int ae^a^u du$$ ? Assuming a is a non-zero constant?

EDIT: Never mind! I figured this out backwards.

$$\frac {d}{du} e^a^u = ae^a^u du$$

Thus

$$\int ae^a^u du = e^a^u$$

Last edited: May 9, 2005
2. May 9, 2005

### rune

You can use substitution.
$$y=au\Rightarrow \frac{dy}{du}=a\Rightarrow du=\frac{dy}{a}$$
Therefore,
$$\int ae^{au}du=\int ae^{y}\frac{1}{a}dy=\int e^{y}dy=e^{y}+C=e^{au}+C$$