en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of e^-x^2

Solution

integral

e^{-} x^{2}

Solution

\frac{e ^{-} x ^{3}}{3} + C

Solution steps

\int e^{-} x^{2} d x

Take the constant out:

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

= e^{-} \cdot \int x^{2} d x

Apply the Power Rule

= e^{-} \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{-} x ^{3}}{3}

Add a constant to the solution

= \frac{e ^{-} x ^{3}}{3} + C

Graph

Popular Examples

integral of ((x-1))/(sqrt(81-4x^2))

integral of 1/(1+9cos(x))

integral of (5x-2)/(x(-2))

integral of (5x^2)/((x-3)^3)

integral of (6x^2-11x+7)/(3x-1)

Frequently Asked Questions (FAQ)

What is the integral of e^-x^2 ?
The integral of e^-x^2 is (e^-x^3)/3+C