What is the integral of e^{-(x^2)/2}x ?

The integral of e^{-(x^2)/2}x is -e^{-(x^2)/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-(x^2)/2}x

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

- e^{- \frac{x ^{2}}{2}} + C

Solution steps

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

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

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

= - \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - e^{u}

Substitute back

u = - \frac{x ^{2}}{2}

= - e^{- \frac{x ^{2}}{2}}

Add a constant to the solution

= - e^{- \frac{x ^{2}}{2}} + C

\int 4 x + 4 d x

\int 2 cos (2 x + \frac{π}{2}) d x

\int \frac{2 y}{( y ^{2} + 1 )} d y

\int x^{4} + e^{4 x} d x

\int \frac{e ^{x}}{2 ( 1 + e ^{x} )} d x

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