What is the integral of (2xe^x-y+6x^2) ?

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

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integral of (2xe^x-y+6x^2)

\int (2 x e^{x} - y + 6 x^{2}) d x

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

Solution steps

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

\int y d x = y x

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

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

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

Add a constant to the solution

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

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