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

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

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

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

120

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 120)

Simplify

= 120

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