# Evaluate the integral # int \ 1/(1+e^x) \ dx # ?

# int \ 1/(1+e^x) \ dx = -ln |1+e^(-x)| + C #

We seek:

Execute the replacement:

Subsequently, the integral turns into:

which, since it is now trivial, allows us to integrate to obtain:

And putting the replacement back in place:

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the integral (\int \frac{1}{1+e^x} , dx), we can use the technique of substitution.

Let (u = 1 + e^x), then (du = e^x , dx).

Rewriting the integral in terms of (u), we have (\int \frac{1}{u} , du).

Integrating (\frac{1}{u}) with respect to (u), we get (\ln|u| + C), where (C) is the constant of integration.

Substituting back (u = 1 + e^x), we have (\ln|1 + e^x| + C) as the antiderivative.

So, (\int \frac{1}{1+e^x} , dx = \ln|1 + e^x| + C).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you integrate #int 1/((x+7)(x^2+9))# using partial fractions?
- How do you use partial fraction decomposition to decompose the fraction to integrate #(16x^4)/(2x-1)^3#?
- How do you find the integral of #int 1/sqrt(1-(x+1)^2)dx#?
- How do you integrate #int (4x^2+6x-2)/((x-1)(x+1)^2)# using partial fractions?
- How do you integrate #int (x^2+1)/((x-3)(x^3-x^2)) dx# using partial fractions?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7