What is the integral from 0 to infinity of x^5e^{-x} ?

The integral from 0 to infinity of x^5e^{-x} is 120

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of x^5e^{-x}

\int_{0}^{\infty} x^{5} e^{- x} d x

120

Solution steps

\int_{0}^{\infty} x^{5} e^{- x} d x

Compute the indefinite integral:

\int x^{5} e^{- x} d x = - e^{- x} x^{5} - 5 (e^{- x} x^{4} - 4 (- e^{- x} x^{3} - 3 (e^{- x} x^{2} - 2 (- e^{- x} x - e^{- x})))) + C

Compute the boundaries:

\int_{0}^{\infty} x^{5} e^{- x} d x = 0 - (- 120)

= 0 - (- 120)

Simplify

= 120

\frac{\partial}{\partial x} (x^{10} + x y^{11} + 9)

\frac{d}{d x} (\frac{2 x}{1 + 4 x ^{2} + 9 x ^{4}})

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

\int_{0}^{2} \frac{x}{8} d x

\frac{\partial}{\partial y} (2 x - x^{3} + 3 x y^{2})

What is the integral from 0 to infinity of x^5e^{-x} ?
The integral from 0 to infinity of x^5e^{-x} is 120