# Indefinite integral

## Homework Statement

∫(exp(6x))/(exp(12x)+25)dx

## The Attempt at a Solution

honestly, don't know where to start. i was looking at another forum and tried to set u=exp(x) du=exp(x) and dx=du/u. plugging that in i got u^6/(u^12+25)*du/u. not sure where to go from there or if that is even the way to go.

Related Calculus and Beyond Homework Help News on Phys.org
gabbagabbahey
Homework Helper
Gold Member
Hi supraboy, Welcome to PF!

Try the substitution $$u=e^{6x}$$ instead

Try setting u = e6x. Then du = 6e6x and e12x = u2.

ok, setting u=e^6x du=6e^6x, then dx=du/6u?

then, it would be int(u/u^2+25)du

using the formula int(a^2+u^2) = (1/a)arctan(u/a) + C

i get, (1/5)arctan(e^6x/5)dx or (1/30)arctan(e^6x/5) + C

this is incorrect though because the answer is negative and it should be arctan(5/e^6x) instead of arctan(e^6x/5).

any ideas?

Last edited:
You made a mistake with the substitution. Write your integral like this:
$$\int \frac{(e^{6x} dx)}{(e^{6x})^2 + 25}$$
If $$u = e^{6x}$$, then $$e^{6x} dx = \frac{1}{6} du$$. Try working from there.