Input
x + 2 y + 3 z
Geometric figure
plane
Real root
z = -x/3 – (2 y)/3
Root
z = -x/3 – (2 y)/3
Integer root
y = 3 n + x, z = -2 n – x, n element Z
Root for the variable z
z = 1/3 (-x – 2 y)
Derivative
(d)/(dx)(x + 2 y + 3 z) = 1
Indefinite integral
integral (x + 2 y + 3 z) dx = x^2/2 + 2 x y + 3 x z + constant
Definite integral over a cube of edge length 2 L
integral_(-L)^L integral_(-L)^L integral_(-L)^L (x + 2 y + 3 z) dz dy dx = 0