- #1
menco
- 43
- 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.
menco said:so if I let u=1+e^-x?
menco said:I still can't figure it out so I gave up and will try again later
The integral of e^-x/(1+e^-x)dx represents the area under the curve of the function e^-x/(1+e^-x) from 0 to infinity.
The integral of e^-x/(1+e^-x)dx can be solved using the substitution method, where u = 1+e^-x and du = -e^-x dx. This will simplify the integral to -1/u du, which can then be solved using the natural logarithm function.
Yes, the integral can also be solved using integration by parts or the partial fractions method.
The integral of e^-x/(1+e^-x)dx is valid for all real numbers.
Yes, the integral can represent the average value of a function over a given interval or the expected value of a random variable in a certain distribution.