Optimal. Leaf size=33 \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{8} B c x^8 \]
[Out]
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Rubi [A] time = 0.121096, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{8} B c x^8 \]
Antiderivative was successfully verified.
[In] Int[x*(A + B*x^2)*(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{A b \int ^{x^{2}} x\, dx}{2} + \frac{B c x^{8}}{8} + x^{6} \left (\frac{A c}{6} + \frac{B b}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(B*x**2+A)*(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.0119226, size = 33, normalized size = 1. \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{8} B c x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x*(A + B*x^2)*(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0., size = 28, normalized size = 0.9 \[{\frac{Ab{x}^{4}}{4}}+{\frac{ \left ( Ac+Bb \right ){x}^{6}}{6}}+{\frac{Bc{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(B*x^2+A)*(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 1.37073, size = 36, normalized size = 1.09 \[ \frac{1}{8} \, B c x^{8} + \frac{1}{6} \,{\left (B b + A c\right )} x^{6} + \frac{1}{4} \, A b x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19886, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{4} x^{4} b A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.042262, size = 29, normalized size = 0.88 \[ \frac{A b x^{4}}{4} + \frac{B c x^{8}}{8} + x^{6} \left (\frac{A c}{6} + \frac{B b}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(B*x**2+A)*(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.218945, size = 39, normalized size = 1.18 \[ \frac{1}{8} \, B c x^{8} + \frac{1}{6} \, B b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{4} \, A b x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*(B*x^2 + A)*x,x, algorithm="giac")
[Out]