1. exponential integral

What do I do when the power in the numerator is larger than the denomenator

e^16x / 4+e^8x

2. Originally Posted by gammaman
What do I do when the power in the numerator is larger than the denomenator

e^16x / 4+e^8x
What do you mean by evaluate? What are you trying to do? Differentiate? Partial fractions? Integrate? Simplify?

3. Oh, sorry I am trying to integrate.

4. Originally Posted by gammaman
Oh, sorry I am trying to integrate.
You can write it:

$\displaystyle \int \frac{(e^{8x})^2}{e^{8x}+4} dx$

5. Ok, and then from there I would do my normal substitution?

6. Originally Posted by gammaman
Ok, and then from there I would do my normal substitution?
I think so, yes.

$\displaystyle u = e^{8x}$

$\displaystyle \frac{du}{dx} = 8e^{8x}$

$\displaystyle dx = \frac{du}{8e^{8x}} = \frac{du}{8u}$

$\displaystyle \int \frac{u^2}{u+4}\frac{du}{8u}$

$\displaystyle = \frac{1}{8} \int\frac{u}{u+4} du$

$\displaystyle = \frac{1}{8} \int\frac{u+4}{u+4} - \frac{4}{u+4} du$

$\displaystyle = \frac{1}{8} \int 1 - \frac{4}{u+4} du$