What is the integral of-2xe^x-6x^2 ?

The integral of-2xe^x-6x^2 is -2(e^xx-e^x)-2x^3+C

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integral of-2xe^x-6x^2

\int - 2 x e^{x} - 6 x^{2} d x

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

Solution steps

\int - 2 x e^{x} - 6 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 2 x e^{x} d x - \int 6 x^{2} d x

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

\int 6 x^{2} d x = 2 x^{3}

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

Add a constant to the solution

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

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What is the integral of-2xe^x-6x^2 ?
The integral of-2xe^x-6x^2 is -2(e^xx-e^x)-2x^3+C