(24 (5 s^4 - 10 s^2 + 1))/(s^2 + 1)^5

(24 (5 (s^2 - 2) s^2 + 1))/(s^2 + 1)^5

((120 s^2 - 240) s^2 + 24)/(((((s^2 + 5) s^2 + 10) s^2 + 10) s^2 + 5) s^2 + 1)

-(240 s^2)/(s^2 + 1)^5 + 24/(s^2 + 1)^5 + (120 s^4)/(s^2 + 1)^5

(120 s^4 - 240 s^2 + 24)/(s^10 + 5 s^8 + 10 s^6 + 10 s^4 + 5 s^2 + 1)

(120 s^4)/(s^10 + 5 s^8 + 10 s^6 + 10 s^4 + 5 s^2 + 1) - (240 s^2)/(s^10 + 5 s^8 + 10 s^6 + 10 s^4 + 5 s^2 + 1) + 24/(s^10 + 5 s^8 + 10 s^6 + 10 s^4 + 5 s^2 + 1)

120/(s^2 + 1)^3 - 480/(s^2 + 1)^4 + 384/(s^2 + 1)^5

s = -sqrt(1 - 2/sqrt(5))

s = sqrt(1 - 2/sqrt(5))

s = -sqrt(1 + 2/sqrt(5))

s = sqrt(1 + 2/sqrt(5))

even

24 - 360 s^2 + 1680 s^4 + O(s^6) (Taylor series)

120/s^6 - 840/s^8 + 3024/s^10 - 7920/s^12 + O((1/s)^13) (Laurent series)

d/ds((24 (5 s^4 - 10 s^2 + 1))/(s^2 + 1)^5) = -(240 s (3 s^4 - 10 s^2 + 3))/(s^2 + 1)^6

integral(24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5 ds = (24 (s - s^3))/(s^2 + 1)^4 + constant

min{(24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5} = -81/8 at s = 1/sqrt(3)

min{(24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5} = -81/8 at s = -1/sqrt(3)

max{(24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5} = 24 at s = 0

lim_(s-> ± ∞) (24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5 = 0

integral_0^∞ (24 (1 - 10 s^2 + 5 s^4))/(1 + s^2)^5 ds≈-2.44942954807925×10^-15...