Optimal. Leaf size=42 \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0704359, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{B c x^{4}}{4} + a \int A\, dx + x^{3} \left (\frac{A c}{3} + \frac{B b}{3}\right ) + \left (A b + B a\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0236573, size = 42, normalized size = 1. \[ \frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4 \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 37, normalized size = 0.9 \[ aAx+{\frac{ \left ( Ab+aB \right ){x}^{2}}{2}}+{\frac{ \left ( Ac+bB \right ){x}^{3}}{3}}+{\frac{Bc{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.690925, size = 49, normalized size = 1.17 \[ \frac{1}{4} \, B c x^{4} + \frac{1}{3} \,{\left (B b + A c\right )} x^{3} + A a x + \frac{1}{2} \,{\left (B a + A b\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.236446, size = 1, normalized size = 0.02 \[ \frac{1}{4} x^{4} c B + \frac{1}{3} x^{3} b B + \frac{1}{3} x^{3} c A + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.090538, size = 39, normalized size = 0.93 \[ A a x + \frac{B c x^{4}}{4} + x^{3} \left (\frac{A c}{3} + \frac{B b}{3}\right ) + x^{2} \left (\frac{A b}{2} + \frac{B a}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.267283, size = 54, normalized size = 1.29 \[ \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A),x, algorithm="giac")
[Out]