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

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

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integral of x+x^2+y^2

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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