x (x^2 - 5) + 1

x≈-2.3301

x≈0.20164

x≈2.1284

Δ = 473

R (all real numbers)

R (all real numbers)

surjective onto R

d/dx(1 - 5 x + x^3) = 3 x^2 - 5

integral(1 - 5 x + x^3) dx = x^4/4 - (5 x^2)/2 + x + constant

min{1 - 5 x + x^3} = 1 - (10 sqrt(5/3))/3 at x = sqrt(5/3)

max{1 - 5 x + x^3} = 1 + (10 sqrt(5/3))/3 at x = -sqrt(5/3)

integral_(root of 1 - 5 x + x^3 near x = -2.33006)^(root of 1 - 5 x + x^3 near x = 0.20164) (1 - 5 x + x^3) dx = 1/4 sqrt(1/6 (3580 + 1602050/(1/2 (1423408309 + 4581951 i sqrt(1419)))^(1/3) + 2^(2/3) (1423408309 + 4581951 i sqrt(1419))^(1/3)))≈8.63442

integral_(root of 1 - 5 x + x^3 near x = 0.20164)^(root of 1 - 5 x + x^3 near x = 2.12842) (1 - 5 x + x^3) dx = -((-1)^(1/4) sqrt(-7160 i + (1602050 i)/(1/2 (1423408309 + 4581951 i sqrt(1419)))^(1/3) - (1602050 sqrt(3))/(1/2 (1423408309 + 4581951 i sqrt(1419)))^(1/3) + i 2^(2/3) (1423408309 + 4581951 i sqrt(1419))^(1/3) + 2^(2/3) sqrt(3) (1423408309 + 4581951 i sqrt(1419))^(1/3)))/(8 sqrt(3))≈-4.1668