What is the integral of 3x^2y^2-10xy^2 ?

The integral of 3x^2y^2-10xy^2 is -5y^2x^2+y^2x^3+C

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integral of 3x^2y^2-10xy^2

\int 3 x^{2} y^{2} - 10 x y^{2} d x

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

Solution steps

\int 3 x^{2} y^{2} - 10 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 10 y^{2} x d x + \int 3 y^{2} x^{2} d x

\int 10 y^{2} x d x = 5 y^{2} x^{2}

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

= - 5 y^{2} x^{2} + y^{2} x^{3}

Add a constant to the solution

= - 5 y^{2} x^{2} + y^{2} x^{3} + C

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What is the integral of 3x^2y^2-10xy^2 ?
The integral of 3x^2y^2-10xy^2 is -5y^2x^2+y^2x^3+C