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

The integral of xe^{-x^2+2} is -1/2 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 xe^{-x^2+2}

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - x^{2} + 2

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

Add a constant to the solution

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

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

\int 9 cot (x) sin (x) d x

\int (x 3 x) d x

\int \frac{a ^{2} x ^{2}}{x ^{3} + a} d x

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

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