(8x+3y+67)/sqrt(8^2+3^2)

(8x+3y+67)/sqrt(8^2+3^2)

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)

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