What is the integral of (4x^3y^2-2xy^3) ?

The integral of (4x^3y^2-2xy^3) is -y^3x^2+y^2x^4+C

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integral of (4x^3y^2-2xy^3)

\int (4 x^{3} y^{2} - 2 x y^{3}) d x

- y^{3} x^{2} + y^{2} x^{4} + C

Solution steps

\int 4 x^{3} y^{2} - 2 x y^{3} 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 y^{3} x d x + \int 4 y^{2} x^{3} d x

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

\int 4 y^{2} x^{3} d x = y^{2} x^{4}

= - y^{3} x^{2} + y^{2} x^{4}

Add a constant to the solution

= - y^{3} x^{2} + y^{2} x^{4} + C

\frac{d}{d x} (5^{s i n (3 x)})

x ln (\frac{x}{y}) d y - y d x = 0

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 4}{x})

f (x) = 6 x e^{x}

\frac{d}{d x} ((x^{4} - 1) (x^{2} + 1))

What is the integral of (4x^3y^2-2xy^3) ?
The integral of (4x^3y^2-2xy^3) is -y^3x^2+y^2x^4+C