integral of integral of integral of z^2

Soluzione

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

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

Fasi della soluzione

\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

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

\int \int 3 x d x d x

\int \int e^{- (x + y)} d x d y

\int \int 8 x^{3} + 2 y^{2} d y d x

\int \int x + y d x d y