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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

\int \frac{3 + 6 x}{1 + x ^{2}} d x

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\frac{d}{d x} (\frac{4}{1 + x})

\int \frac{8}{x ( ln ( x ) + 1 ) ^{\frac{3}{2}}} d x

3 x - 4

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