What is the integral of 3x^2-2x-y ?

The integral of 3x^2-2x-y is -yx-x^2+x^3+C

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integral of 3x^2-2x-y

\int 3 x^{2} - 2 x - y d x

- y x - x^{2} + x^{3} + C

Solution steps

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

\int y d x = y x

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

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

= - y x - x^{2} + x^{3}

Add a constant to the solution

= - y x - x^{2} + x^{3} + C