Input 
(8 x + 3 y + 67)/sqrt(8^2 + 3^2) 
Result 
(8 x + 3 y + 67)/sqrt(73) 
Geometric figure 
plane 
Real root 
y = (8 x)/3 – 67/3 
Root 
y = (8 x)/3 – 67/3 
Integer root 
x = 3 n + 1, y = 8 n – 25, n element Z 
Root for the variable y 
y = (8 sqrt(73) x + 67 sqrt(73))/(3 sqrt(73)) 
Derivative 
(d)/(dx)((8 x + 3 y + 67)/sqrt(8^2 + 3^2)) = 8/sqrt(73) 
Indefinite integral 
integral (67 + 8 x + 3 y)/sqrt(73) dx = (4 x^2 + 3 x y + 67 x)/sqrt(73) + constant 
Definite integral over a disk of radius R 
integral integral_(x^2 + y^2

Definite integral over a square of edge length 2 L 
integral_(L)^L integral_(L)^L (67 + 8 x + 3 y)/sqrt(73) dy dx = (268 L^2)/sqrt(73) 