Input
(1 – 2 x + x^2) (-1 + x^2)
Expanded form
x^4 – 2 x^3 + 2 x – 1
Polynomial discriminant
Delta = 0
Derivative
d/dx((1 – 2 x + x^2) (-1 + x^2)) = 2 (x – 1)^2 (2 x + 1)
Indefinite integral
integral (-1 + x^2) (1 – 2 x + x^2) dx = x^5/5 – x^4/2 + x^2 – x + constant
Global minimum
min{(1 – 2 x + x^2) (-1 + x^2)} = -27/16 at x = -1/2
Definite integral
integral_(-1)^1 (-1 + x^2) (1 – 2 x + x^2) dx = -8/5 = -1.6
Definite integral area below the axis between the smallest and largest real roots
integral_(-1)^1 (-1 + x^2) (1 – 2 x + x^2) theta(-(-1 + x^2) (1 – 2 x + x^2)) dx = -8/5 = -1.6