integral of integral of integral of z^2

解

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

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

解答ステップ

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

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

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

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

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

\int ((C + z^{2} x) y + C) d z = C z + y (C z + \frac{x z ^{3}}{3}) + C

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