en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/(e^x)

Solution

\int - \frac{1}{e ^{x}} d x

Solution

\frac{1}{e ^{x}} + C

Solution steps

\int - \frac{1}{e ^{x}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{e ^{x}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = e^{x}

= - (- \frac{1}{e ^{x}})

Simplify

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

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches-2 of |1-x^2|

x \to - 2 lim (1 - x^{2})

integral of (x+2)/(x^2+16)

\int \frac{x + 2}{x ^{2} + 16} d x

derivative of sqrt(1/(x^{25)})

\frac{d}{d x} (\frac{1}{x ^{25}})

slope ofintercept (3,-5),(-1,3)slope intercept

(3, - 5), (- 1, 3)

derivative of sin^7(cos(5x))derivative of

sin^{7} (cos (5 x))

Frequently Asked Questions (FAQ)

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