What is the integral of e^{-t}t ?

The integral of e^{-t}t is -e^{-t}t-e^{-t}+C

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integral of e^{-t}t

\int e^{- t} t d t

- e^{- t} t - e^{- t} + C

Solution steps

\int e^{- t} t d t

Apply Integration By Parts

: - e^{- t} t - \int - e^{- t} d t

= - e^{- t} t - \int - e^{- t} d t

\int - e^{- t} d t = e^{- t}

= - e^{- t} t - e^{- t}

Add a constant to the solution

= - e^{- t} t - e^{- t} + C

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