integral of integral of integral of xyz

Lösung

\int \int \int x yz d x d y d z

C z + \frac{y ^{2} x ^{2} z ^{2}}{8} + C yz + C

Schritte zur Lösung

\int \int \int x yz d x d y d z

\int x yz d x = \frac{yz x ^{2}}{2} + C

= \int \int (\frac{yz x ^{2}}{2} + C) d y d z

\int (\frac{yz x ^{2}}{2} + C) d y = C y + \frac{z x ^{2} y ^{2}}{4} + C

= \int (C y + \frac{z x ^{2} y ^{2}}{4} + C) d z

\int (C y + \frac{z x ^{2} y ^{2}}{4} + C) d z = C z + \frac{y ^{2} x ^{2} z ^{2}}{8} + C yz + C

= C z + \frac{y ^{2} x ^{2} z ^{2}}{8} + C yz + C

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