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

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

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

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

Solution steps

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

Simplify

= \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 x^{3} + x^{2} + x + 1 d x

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

\int \frac{1}{b ^{2} x ^{2} - a ^{2}} d x

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

\int 4 sin (\frac{x}{3}) d x

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