Recognitions:
Gold Member
Homework Help

## integral sign error

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

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

The second integral can be done by the substitution
$$u = 1-e^x$$
$$du = -e^x dx$$

So the second integral becomes:
$$\int \frac{du}{u} = \ln|u|+C$$
In the first integral, you can use the substituion:
$$w = e^x$$
$$dw = e^x dx$$

So the first integral becomes:
$$\int \frac{dw}{w(1-w)}$$
This can be done by parts and you get:
$$\int \frac{dw}{w} + \int \frac{dw}{1-w}$$

These are also both natural logs so you end up with:

$$\ln|e^x| - 2\ln|1-e^x| + C$$

$$x - 2\ln|1-e^x| +C$$

I had http://integrals.wolfram.com/index.jsp compute this for me and it got:

$$x - 2\ln(e^x - 1) +C$$

I think this may have something to do with the absolute value, but I always make stupid mistakes with signs so I thought I'd check.....Thanks for the time I probably just wasted.
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
 Recognitions: Gold Member Homework Help For some reason it won't let me edit my post..... on the fifth line that integral should be $$-\int\frac{du}{u}$$
 Recognitions: Homework Help sure, |a-b|=|b-a|

Recognitions:
Gold Member
Homework Help

## integral sign error

ok thanks alot, stupid question

 Similar discussions for: integral sign error Thread Forum Replies Calculus 13 Calculus 3 Differential Geometry 0 Calculus 2 Calculus 4