Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{8} b B x^8 \]
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Rubi [A] time = 0.0623301, antiderivative size = 33, 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 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{8} b B x^8 \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^3)*(A + B*x^3),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \int x\, dx + \frac{B b x^{8}}{8} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**3+a)*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.010034, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{8} b B x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^3)*(A + B*x^3),x]
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Maple [A] time = 0., size = 28, normalized size = 0.9 \[{\frac{aA{x}^{2}}{2}}+{\frac{ \left ( Ab+Ba \right ){x}^{5}}{5}}+{\frac{bB{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^3+a)*(B*x^3+A),x)
[Out]
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Maxima [A] time = 1.37498, size = 36, normalized size = 1.09 \[ \frac{1}{8} \, B b x^{8} + \frac{1}{5} \,{\left (B a + A b\right )} x^{5} + \frac{1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x,x, algorithm="maxima")
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Fricas [A] time = 0.203789, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{2} x^{2} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.076719, size = 29, normalized size = 0.88 \[ \frac{A a x^{2}}{2} + \frac{B b x^{8}}{8} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**3+a)*(B*x**3+A),x)
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GIAC/XCAS [A] time = 0.220171, size = 39, normalized size = 1.18 \[ \frac{1}{8} \, B b x^{8} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{2} \, A a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)*x,x, algorithm="giac")
[Out]