What is the integral of 6xy^2-y^3 ?

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

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integral of 6xy^2-y^3

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

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

Solution steps

\int 6 x y^{2} - 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 y^{3} d x + \int 6 y^{2} x d x

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

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

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

Add a constant to the solution

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

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