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

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

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integral of a(x^2+y^2)

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

a (y^{2} x + \frac{x ^{3}}{3}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= a \cdot \int y^{2} + 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

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

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

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

= a (y^{2} x + \frac{x ^{3}}{3})

Add a constant to the solution

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

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