Optimal. Leaf size=74 \[ \frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{6} x^6 (A c+b C)+\frac{1}{5} b B x^5+\frac{1}{7} B c x^7+\frac{1}{8} c C x^8 \]
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Rubi [A] time = 0.117787, antiderivative size = 74, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{6} x^6 (A c+b C)+\frac{1}{5} b B x^5+\frac{1}{7} B c x^7+\frac{1}{8} c C x^8 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \int x\, dx + \frac{B a x^{3}}{3} + \frac{B b x^{5}}{5} + \frac{B c x^{7}}{7} + \frac{C c x^{8}}{8} + x^{6} \left (\frac{A c}{6} + \frac{C b}{6}\right ) + x^{4} \left (\frac{A b}{4} + \frac{C a}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(C*x**2+B*x+A)*(c*x**4+b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.0221838, size = 74, normalized size = 1. \[ \frac{1}{4} x^4 (a C+A b)+\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{6} x^6 (A c+b C)+\frac{1}{5} b B x^5+\frac{1}{7} B c x^7+\frac{1}{8} c C x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 61, normalized size = 0.8 \[{\frac{aA{x}^{2}}{2}}+{\frac{aB{x}^{3}}{3}}+{\frac{ \left ( Ab+aC \right ){x}^{4}}{4}}+{\frac{bB{x}^{5}}{5}}+{\frac{ \left ( Ac+bC \right ){x}^{6}}{6}}+{\frac{Bc{x}^{7}}{7}}+{\frac{cC{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)
[Out]
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Maxima [A] time = 0.703562, size = 81, normalized size = 1.09 \[ \frac{1}{8} \, C c x^{8} + \frac{1}{7} \, B c x^{7} + \frac{1}{5} \, B b x^{5} + \frac{1}{6} \,{\left (C b + A c\right )} x^{6} + \frac{1}{3} \, B a x^{3} + \frac{1}{4} \,{\left (C a + A b\right )} x^{4} + \frac{1}{2} \, A a x^{2} \]
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,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240343, size = 1, normalized size = 0.01 \[ \frac{1}{8} x^{8} c C + \frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} b C + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} b B + \frac{1}{4} x^{4} a C + \frac{1}{4} x^{4} b A + \frac{1}{3} x^{3} a B + \frac{1}{2} x^{2} a A \]
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,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.101254, size = 68, normalized size = 0.92 \[ \frac{A a x^{2}}{2} + \frac{B a x^{3}}{3} + \frac{B b x^{5}}{5} + \frac{B c x^{7}}{7} + \frac{C c x^{8}}{8} + x^{6} \left (\frac{A c}{6} + \frac{C b}{6}\right ) + x^{4} \left (\frac{A b}{4} + \frac{C a}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(C*x**2+B*x+A)*(c*x**4+b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.278687, size = 86, normalized size = 1.16 \[ \frac{1}{8} \, C c x^{8} + \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, C b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{4} \, C a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2} \]
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,x, algorithm="giac")
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