What is the integral of integral of (x+y)^2 ?

The integral of integral of (x+y)^2 is Cy+(x^3)/3 y+(x^2y^2)/2+(xy^3)/3+C

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integral of integral of (x+y)^2

\int \int (x + y)^{2} d x d y

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

Solution steps

\int \int (x + y)^{2} d x d y

\int (x + y)^{2} d x = y^{2} x + y x^{2} + \frac{x ^{3}}{3} + C

= \int (y^{2} x + y x^{2} + \frac{x ^{3}}{3} + C) d y

\int (y^{2} x + y x^{2} + \frac{x ^{3}}{3} + C) d y = C y + \frac{x ^{3}}{3} y + \frac{x ^{2} y ^{2}}{2} + \frac{x y ^{3}}{3} + C

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

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