How Do You Integrate e^-x / (1 + e^-x) dx?

Click For Summary
SUMMARY

The integral of the function (e^-x)/(1 + e^-x) dx can be approached using u-substitution. By letting u = 1 + e^-x, the differential du becomes -e^-x dx. This substitution simplifies the integral and allows for easier computation. Understanding the relationship between u and du is crucial for solving this integral effectively.

PREREQUISITES
  • Understanding of u-substitution in calculus
  • Familiarity with the properties of exponential functions
  • Knowledge of integral calculus techniques
  • Ability to manipulate differentials in integration
NEXT STEPS
  • Practice u-substitution with various functions
  • Study the properties of exponential integrals
  • Learn about integration techniques for rational functions
  • Explore advanced integration methods such as integration by parts
USEFUL FOR

Students studying calculus, particularly those tackling integration problems involving exponential functions and seeking to improve their problem-solving skills in integral calculus.

menco
Messages
42
Reaction score
0

Homework Statement


(e^-x)/(1+e^-x)dx


Homework Equations


Integral of e^x function


The Attempt at a Solution


I am completely lost with the problem, the fact that it is e^-x and not e^x has me stupped as well as the division.
 
Physics news on Phys.org
Try u-substitution.
 
so if I let u=1+e^-x?
 
yes?
 
menco said:
so if I let u=1+e^-x?

Well, does it work?
 
I still can't figure it out so I gave up and will try again later
 
menco said:
I still can't figure it out so I gave up and will try again later

When you do get back to it, answer this: What is du when u=1+e^{-x}?
 
Will du = -e^-x dx
 

Similar threads

Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
The indefinite integral and its "argument"
  • · Replies 3 ·
Replies
3
Views
2K
Should the Units of a Constant Match the Integral Boundary Conditions?
  • · Replies 5 ·
Replies
5
Views
1K
How can the indefinite integral of e^(1/x)/(x(x+1)^2) be solved by hand?
  • · Replies 2 ·
Replies
2
Views
2K
How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?
  • · Replies 9 ·
Replies
9
Views
2K
Arc length of vector function - the integral seems impossible
  • · Replies 2 ·
Replies
2
Views
2K
Integral of e^cosx: Answers Sought
  • · Replies 11 ·
Replies
11
Views
3K
How should I show that all solutions are periodic?
  • · Replies 10 ·
Replies
10
Views
2K
First Order Diffy Q Problem with Bernoulli/Integrating Factors
  • · Replies 4 ·
Replies
4
Views
2K
Compute the integral of the Gaussian
  • · Replies 3 ·
Replies
3
Views
2K