en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of 1/(1+e^x)

Solution

\int_{- 1}^{1} \frac{1}{1 + e ^{x}} d x

Solution

1

Solution steps

\int_{- 1}^{1} \frac{1}{1 + e ^{x}} d x

\frac{1}{1 + e ^{x}} = - \frac{e ^{x}}{1 + e ^{x}} + 1

= \int_{- 1}^{1} - \frac{e ^{x}}{1 + e ^{x}} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 1}^{1} \frac{e ^{x}}{1 + e ^{x}} d x + \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} \frac{e ^{x}}{1 + e ^{x}} d x = 1

\int_{- 1}^{1} 1 d x = 2

= - 1 + 2

Simplify

= 1

Popular Examples

integral from 0 to 1 of x(x+5)

\int_{0}^{1} x (x + 5) d x

integral from 0 to 1 of 2/3 x

\int_{0}^{1} \frac{2}{3} x d x

integral from-2 to 3 of (x+6-x^2)

\int_{- 2}^{3} (x + 6 - x^{2}) d x

integral from 0 to pi of 9xcos(3x)

\int_{0}^{π} 9 x cos (3 x) d x

integral from 0 to 2 of 6e^x

\int_{0}^{2} 6 e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of 1/(1+e^x) ?
The integral from-1 to 1 of 1/(1+e^x) is 1