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

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

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integral of (3y^2-2xy)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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