What is the integral of xe^{-3x^2} ?

The integral of xe^{-3x^2} is -1/6 e^{-3x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xe^{-3x^2}

\int x e^{- 3 x^{2}} d x

- \frac{1}{6} e^{- 3 x^{2}} + C

Solution steps

\int x e^{- 3 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 3 x^{2}

= - \frac{1}{6} e^{- 3 x^{2}}

Add a constant to the solution

= - \frac{1}{6} e^{- 3 x^{2}} + C

\int_{0}^{2} \frac{1}{x ^{2} - 2 x + 2} d x

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

\int (sin (x))^{2} cos (x) d x

x \to 0 lim (\frac{0}{2 x ^{2}})

\frac{d y}{d t} = sin (t) - y, y (0) = - 1

What is the integral of xe^{-3x^2} ?
The integral of xe^{-3x^2} is -1/6 e^{-3x^2}+C