What is the integral of e^{-x}(2x+1) ?

The integral of e^{-x}(2x+1) is -2e^{-x}x-3e^{-x}+C

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integral of e^{-x}(2x+1)

\int e^{- x} (2 x + 1) d x

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

Solution steps

\int e^{- x} (2 x + 1) d x

Apply Integration By Parts

= - e^{- x} (2 x + 1) - \int - 2 e^{- x} d x

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

= - e^{- x} (2 x + 1) - 2 e^{- x}

Simplify

- e^{- x} (2 x + 1) - 2 e^{- x} : - 2 e^{- x} x - 3 e^{- x}

= - 2 e^{- x} x - 3 e^{- x}

Add a constant to the solution

= - 2 e^{- x} x - 3 e^{- x} + C

What is the integral of e^{-x}(2x+1) ?
The integral of e^{-x}(2x+1) is -2e^{-x}x-3e^{-x}+C