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

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

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integral of (x+y)^2

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

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

Solution steps

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

Expand

(y + x)^{2} : y^{2} + 2 y x + x^{2}

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

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

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

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

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

Add a constant to the solution

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

x \to 0 lim (\frac{sin ( 4 x )}{tan ( 3 x )})

\int_{1}^{\infty} 12 e^{- 6 x} d x

\frac{10 s ^{2}}{s ^{2} + 9}

x \to 1 lim (x^{2} + 5)

y^{^{'}} = x + 4 y - 2

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