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

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

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

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

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

Solution steps

\int 3 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 e^{- x} d x

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

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

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

Add a constant to the solution

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

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