What is the integral of 3x^2-4x+2-e^{-x} ?

The integral of 3x^2-4x+2-e^{-x} is x^3-2x^2+2x+e^{-x}+C

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integral of 3x^2-4x+2-e^{-x}

\int 3 x^{2} - 4 x + 2 - e^{- x} d x

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

Solution steps

\int 3 x^{2} - 4 x + 2 - e^{- x} d x

Apply the Sum Rule:

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

= \int 3 x^{2} d x - \int 4 x d x + \int 2 d x - \int e^{- x} d x

\int 3 x^{2} d x = x^{3}

\int 4 x d x = 2 x^{2}

\int 2 d x = 2 x

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

= x^{3} - 2 x^{2} + 2 x - (- e^{- x})

Simplify

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

Add a constant to the solution

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

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What is the integral of 3x^2-4x+2-e^{-x} ?
The integral of 3x^2-4x+2-e^{-x} is x^3-2x^2+2x+e^{-x}+C