What is the integral from 0 to infinity of x^9e^{-x} ?

The integral from 0 to infinity of x^9e^{-x} is 362880

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integral from 0 to infinity of x^9e^{-x}

\int_{0}^{\infty} x^{9} e^{- x} d x

362880

Solution steps

\int_{0}^{\infty} x^{9} e^{- x} d x

Compute the indefinite integral:

\int x^{9} e^{- x} d x = - e^{- x} x^{9} - 9 (e^{- x} x^{8} - 8 (- e^{- x} x^{7} - 7 (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^{9} e^{- x} d x = 0 - (- 362880)

= 0 - (- 362880)

Simplify

= 362880

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What is the integral from 0 to infinity of x^9e^{-x} ?
The integral from 0 to infinity of x^9e^{-x} is 362880