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

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

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integral of (3x^2-2xy+2)

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

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

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