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

The integral of (-4x^3+e^{-2x}+sqrt(2)) is -x^4-1/2 e^{-2x}+sqrt(2)x+C

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

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

- x^{4} - \frac{1}{2} e^{- 2 x} + 2 x + C

Solution steps

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

\int 4 x^{3} d x = x^{4}

\int e^{- 2 x} d x = - \frac{1}{2} e^{- 2 x}

\int 2 d x = 2 x

= - x^{4} - \frac{1}{2} e^{- 2 x} + 2 x

Add a constant to the solution

= - x^{4} - \frac{1}{2} e^{- 2 x} + 2 x + C

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What is the integral of (-4x^3+e^{-2x}+sqrt(2)) ?
The integral of (-4x^3+e^{-2x}+sqrt(2)) is -x^4-1/2 e^{-2x}+sqrt(2)x+C