What is the integral from 0 to infinity of x^6e^{-x} ?

The integral from 0 to infinity of x^6e^{-x} is 720

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^6e^{-x}

\int_{0}^{\infty} x^{6} e^{- x} d x

720

Solution steps

\int_{0}^{\infty} x^{6} e^{- x} d x

Compute the indefinite integral:

\int x^{6} e^{- x} d x = - e^{- x} x^{6} + 6 (- 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^{6} e^{- x} d x = 0 - (- 720)

= 0 - (- 720)

Simplify

= 720

\int_{0}^{\infty} cos (π) x d x

\int_{0}^{\frac{π}{4}} sin^{2} (θ) d θ

\int_{0}^{\infty} λ e^{- λ x} d x

\int_{0}^{1} (x^{3} + 3 x + 4) d x

\int_{- 2}^{2} 4 - y^{2} d y

What is the integral from 0 to infinity of x^6e^{-x} ?
The integral from 0 to infinity of x^6e^{-x} is 720