help with this integral: int e^(4x) / (e^(3x) + 25) dx

[crikket]

So what I've got is an indefinite integral,

e^(4x) / (e^(8x) + 25) dx

I've been trying to do this by u-substition, where u=e^(4x) but I can't seem to get the right answer. I know that there must be some significance in the fact that (e^(4x))^2 is e^(8x), but I'm just not getting it. Any suggestions would be wonderful.

 

[pka]

This is arctangent form.
\(\displaystyle \frac{{du}}{{u^2 + 1}}.\)

 

[crikket]

Ah, yes that certainly helps.

So, I ended up with 1/20 arctan(e^(4x)/5) + C
Thanks for your help!