# Homework Help: Misc integral

1. Mar 29, 2010

### nameVoid

$$\int \frac{1+e^x}{1-e^x}dx$$
$$\int \frac{dx}{1-e^x} +\int \frac{e^x}{1-e^x}dx$$
$$u=e^x$$
$$lnu=x$$
$$\frac{du}{u}=dx$$
$$\int \frac{du}{u(1-u)}+\int \frac{du}{1-u}$$
$$\int \frac{A}{u}+\frac{B}{1-u}du -ln|1-u|+C$$
$$ln|e^x|+ln|1-e^x|-ln|1-e^x|+C$$
$$x+C$$
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 29, 2010

### Staff: Mentor

Your antiderivative is obviously incorrect, since d/dx(x + C) = 1. Your antiderivative would have been correct if its derivative was (1 + e^x)/(1 - e^x).

It might be easier not to split into two integrals, but using the same substitution. If you do that, you'll get something you can use partial decomposition on.

3. Mar 30, 2010

### nameVoid

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