# Finding the antiderivative of a fractional prob

1. Jan 16, 2009

### MathNoob123

I am suppose to evaluate this integral by using substitution

f'(x)=(e^-0.5x)/(1-e^-.5x)
I will be very thankful if someone were able to tell me a strategy in antiderivitating fractional problems.

What I did:
I set u=-0.5x
dx=du/-0.5

therefore i got (-1/0.5)((e^u)/(1-e^u))du
I am unsure of what the next step would be

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 16, 2009

### Staff: Mentor

Assuming this is the problem:
$$\int \frac{e^{-.5x}}{1 - e^{-.5x}} dx$$

Let u = 1 - e-.5x

Then your integral is more or less
$$\int \frac{du}{u}$$
which is pretty easy.