What is the integral of (2xy-3x^2) ?

The integral of (2xy-3x^2) is -x^3+yx^2+C

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integral of (2xy-3x^2)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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