Optimal. Leaf size=74 \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.15507, antiderivative size = 74, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
Antiderivative was successfully verified.
[In] Int[x^2*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 23.2355, size = 68, normalized size = 0.92 \[ \frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{B b x^{6}}{6} + \frac{B c x^{8}}{8} + \frac{C c x^{9}}{9} + x^{7} \left (\frac{A c}{7} + \frac{C b}{7}\right ) + x^{5} \left (\frac{A b}{5} + \frac{C a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(C*x**2+B*x+A)*(c*x**4+b*x**2+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0339102, size = 74, normalized size = 1. \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 61, normalized size = 0.8 \[{\frac{aA{x}^{3}}{3}}+{\frac{aB{x}^{4}}{4}}+{\frac{ \left ( Ab+aC \right ){x}^{5}}{5}}+{\frac{bB{x}^{6}}{6}}+{\frac{ \left ( Ac+bC \right ){x}^{7}}{7}}+{\frac{Bc{x}^{8}}{8}}+{\frac{cC{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.698025, size = 81, normalized size = 1.09 \[ \frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{6} \, B b x^{6} + \frac{1}{7} \,{\left (C b + A c\right )} x^{7} + \frac{1}{4} \, B a x^{4} + \frac{1}{5} \,{\left (C a + A b\right )} x^{5} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)*x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228166, size = 1, normalized size = 0.01 \[ \frac{1}{9} x^{9} c C + \frac{1}{8} x^{8} c B + \frac{1}{7} x^{7} b C + \frac{1}{7} x^{7} c A + \frac{1}{6} x^{6} b B + \frac{1}{5} x^{5} a C + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a B + \frac{1}{3} x^{3} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)*x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.103473, size = 68, normalized size = 0.92 \[ \frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{B b x^{6}}{6} + \frac{B c x^{8}}{8} + \frac{C c x^{9}}{9} + x^{7} \left (\frac{A c}{7} + \frac{C b}{7}\right ) + x^{5} \left (\frac{A b}{5} + \frac{C a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(C*x**2+B*x+A)*(c*x**4+b*x**2+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.280558, size = 86, normalized size = 1.16 \[ \frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{7} \, A c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, C a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)*x^2,x, algorithm="giac")
[Out]