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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summenregel an:

\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}

Füge eine Konstante zur Lösung hinzu

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

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