Ax 2 bx c

Ax 2 bx c

Input
(a x)×2 (b x) c
Result
2 a b c x^2
Geometric figure
parabola
Polynomial discriminant
Delta = 0
Derivative
(d)/(dx)((a x)×2 (b x) c) = 4 a b c x
Indefinite integral
integral 2 a b c x^2 dx = 2/3 a b c x^3 + constant
Definite integral over a hypersphere of radius R
integral integral integral integral_(a^2 + b^2 + c^2 + x^2
Definite integral over a hypercube of edge length 2 L
integral_(-L)^L integral_(-L)^L integral_(-L)^L integral_(-L)^L 2 a b c x^2 dx dc db da = 0

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