- #1
philipc
- 57
- 0
just wonder if someone could help me solve this integral,
thanks
(e^-2x) / (1+e^-x)
thanks
(e^-2x) / (1+e^-x)
How Do You Solve the Integral of (e^-2x) / (1+e^-x)?
- Thread starter philipc
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SUMMARY
The integral of (e^-2x) / (1 + e^-x) can be solved using algebraic manipulation and substitution techniques. Specifically, substituting t = e^-x simplifies the integral, allowing for the application of U substitution. The transformation leads to a more manageable form, where u = (1 + e^-x) is utilized, and the differential dx must be accounted for. Following these steps will yield the correct solution to the integral.
PREREQUISITES- Understanding of integral calculus
- Familiarity with U substitution technique
- Knowledge of algebraic manipulation
- Basic concepts of exponential functions
- Practice solving integrals using U substitution
- Explore algebraic manipulation techniques for integrals
- Study exponential function properties and their integrals
- Learn about integration techniques for rational functions
Students and professionals in mathematics, particularly those studying calculus and integral techniques, will benefit from this discussion.
- #2
Chen
- 976
- 1
Can you integrate (t2) / (1 + t)? I'm guessing that's how you should do it, since I don't really know... 
- #3
faust9
- 690
- 2
philipc said:
Do some algebraic manipulation of the original problem. If you do, the problem wil reduce to a form that allows U substitution.
- #4
TMcCloskey
- 3
- 0
I think Chen was on the right track, ie, use substitution t = e^-x
but don't forget about dx -- should come to a much simpler integration
but don't forget about dx -- should come to a much simpler integration
- #5
thermodynamicaldude
- 58
- 1
k..substitute u = (1 + e^-x)...then find du...work from there...and you should get the correct answer...
...hint...remember that u-1 = e^-x...
...hint...remember that u-1 = e^-x...
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