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

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

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integral of x^2-e^{-x}

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

\frac{x ^{3}}{3} + e^{- x} + C

Solution steps

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

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

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

= \frac{x ^{3}}{3} - (- e^{- x})

Simplify

= \frac{x ^{3}}{3} + e^{- x}

Add a constant to the solution

= \frac{x ^{3}}{3} + e^{- x} + C

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