What is the integral of 3x^2y+4xy^2 ?

The integral of 3x^2y+4xy^2 is yx^3+2y^2x^2+C

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integral of 3x^2y+4xy^2

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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