What is the integral of (6xy-2y^2+1) ?

The integral of (6xy-2y^2+1) is x-2y^2x+3yx^2+C

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integral of (6xy-2y^2+1)

\int (6 x y - 2 y^{2} + 1) d x

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

Solution steps

\int 6 x y - 2 y^{2} + 1 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 1 d x - \int 2 y^{2} d x + \int 6 y x d x

\int 1 d x = x

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

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

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

Add a constant to the solution

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

\int_{0}^{0.6} 200 x d x

\int tanh (\frac{x}{9}) d x

\frac{d}{d x} (e^{2 x} + sin (x^{2}))

\frac{d}{d x} (4 e^{3 x})

f (x) = (x^{3} + 2 x - 2)^{4}

What is the integral of (6xy-2y^2+1) ?
The integral of (6xy-2y^2+1) is x-2y^2x+3yx^2+C