What is the integral of xe^{-6x^2} ?

The integral of xe^{-6x^2} is -1/12 e^{-6x^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^{-6x^2}

\int x e^{- 6 x^{2}} d x

- \frac{1}{12} e^{- 6 x^{2}} + C

Solution steps

\int x e^{- 6 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{12} d u

= \int - \frac{e ^{u}}{12} d u

Take the constant out:

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

= - \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{12} e^{u}

Substitute back

u = - 6 x^{2}

= - \frac{1}{12} e^{- 6 x^{2}}

Add a constant to the solution

= - \frac{1}{12} e^{- 6 x^{2}} + C

x \to - 2 lim (4 x^{2} - 3 x + 5)

\frac{y ^{2} + 1}{y d y} = \frac{x}{d x}

\frac{d}{d x} (2 x^{2} - 4 x + 5)

\frac{d}{d x} (e^{x} (2 x^{4} + 3 cos (x)))

\frac{d}{d x} (- 2 x^{3} + \frac{8}{x ^{2}} - 6 x - 1)

What is the integral of xe^{-6x^2} ?
The integral of xe^{-6x^2} is -1/12 e^{-6x^2}+C