What is the integral of (3x+1)e^{-x} ?

The integral of (3x+1)e^{-x} is -3e^{-x}x-4e^{-x}+C

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integral of (3x+1)e^{-x}

\int (3 x + 1) e^{- x} d x

- 3 e^{- x} x - 4 e^{- x} + C

Solution steps

\int (3 x + 1) e^{- x} d x

Apply Integration By Parts

: - e^{- x} (3 x + 1) - \int - 3 e^{- x} d x

= - e^{- x} (3 x + 1) - \int - 3 e^{- x} d x

\int - 3 e^{- x} d x = 3 e^{- x}

= - e^{- x} (3 x + 1) - 3 e^{- x}

Simplify

- e^{- x} (3 x + 1) - 3 e^{- x} : - 3 e^{- x} x - 4 e^{- x}

= - 3 e^{- x} x - 4 e^{- x}

Add a constant to the solution

= - 3 e^{- x} x - 4 e^{- x} + C

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What is the integral of (3x+1)e^{-x} ?
The integral of (3x+1)e^{-x} is -3e^{-x}x-4e^{-x}+C