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

The integral of xe^{-ax^2} is -1/(2a)e^{-ax^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^{-ax^2}

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{2 a} d u

= \int - \frac{e ^{u}}{2 a} d u

Take the constant out:

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

= - \frac{1}{2 a} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{2 a} e^{u}

Substitute back

u = - a x^{2}

= - \frac{1}{2 a} e^{- a x^{2}}

Add a constant to the solution

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

y^{^{'}} = 4 e^{x + y}

4 x^{2} - 5 x

\frac{\partial}{\partial x} (sin (x \cdot e^{x^{2} \cdot y}))

\int (sin^{3} (2 t)) cos (2 t) d t

x \to 9 + lim (ln (x^{2} - 81))

What is the integral of xe^{-ax^2} ?
The integral of xe^{-ax^2} is -1/(2a)e^{-ax^2}+C