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

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

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

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

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

Solution steps

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

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

\int 2 x d y = 2 x y

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

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

Add a constant to the solution

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

\int_{0}^{1} - 9 (x^{2} + 1) e^{- x} d x

y = (1 + 2 x)^{2}, (1, 9)

\frac{\partial}{\partial x} (arctan (y x))

\frac{d}{d x} (1 + x)

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

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