What is the integral of 6x^2y+2xy^2 ?

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

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integral of 6x^2y+2xy^2

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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