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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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