What is the integral of te^{-t}-2 ?

The integral of te^{-t}-2 is -e^{-t}t-e^{-t}-2t+C

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integral of te^{-t}-2

\int t e^{- t} - 2 d t

- e^{- t} t - e^{- t} - 2 t + C

Solution steps

\int t e^{- t} - 2 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t e^{- t} d t - \int 2 d t

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

\int 2 d t = 2 t

= - e^{- t} t - e^{- t} - 2 t

Add a constant to the solution

= - e^{- t} t - e^{- t} - 2 t + C

What is the integral of te^{-t}-2 ?
The integral of te^{-t}-2 is -e^{-t}t-e^{-t}-2t+C