Finding the antiderivative of a fractional prob

  • #1
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

Please help

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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Assuming this is the problem:
[tex]\int \frac{e^{-.5x}}{1 - e^{-.5x}} dx[/tex]

Let u = 1 - e-.5x

Then your integral is more or less
[tex]\int \frac{du}{u}[/tex]
which is pretty easy.
 

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