What is the integral of 5xe^{-x^2} ?

The integral of 5xe^{-x^2} is -5/2 e^{-x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5xe^{-x^2}

\int 5 x e^{- x^{2}} d x

- \frac{5}{2} e^{- x^{2}} + C

Solution steps

\int 5 x e^{- x^{2}} d x

Take the constant out:

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

= 5 \cdot \int x e^{- x^{2}} d x

Apply u-substitution

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

= 5 \cdot \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

= 5 (- \frac{1}{2} \cdot \int e^{u} d u)

Use the common integral:

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

= 5 (- \frac{1}{2} e^{u})

Substitute back

u = - x^{2}

= 5 (- \frac{1}{2} e^{- x^{2}})

Simplify

5 (- \frac{1}{2} e^{- x^{2}}) : - \frac{5}{2} e^{- x^{2}}

= - \frac{5}{2} e^{- x^{2}}

Add a constant to the solution

= - \frac{5}{2} e^{- x^{2}} + C

f (x) = \frac{a x + b}{c x + d}

- 24 e^{- 4 x}

4 x, y = 1, x = 0

\frac{d}{d x} ((5 x^{2} + e)^{6})

n = 3 \sum \infty x^{n}

What is the integral of 5xe^{-x^2} ?
The integral of 5xe^{-x^2} is -5/2 e^{-x^2}+C