Optimal. Leaf size=30 \[ \frac{a^2 x^6}{6}+\frac{2}{7} a b x^7+\frac{b^2 x^8}{8} \]
[Out]
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Rubi [A] time = 0.0470887, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^2 x^6}{6}+\frac{2}{7} a b x^7+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[x*(a*x^2 + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 7.52156, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**3+a*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.00316111, size = 30, normalized size = 1. \[ \frac{a^2 x^6}{6}+\frac{2}{7} a b x^7+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a*x^2 + b*x^3)^2,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{6}}{6}}+{\frac{2\,ab{x}^{7}}{7}}+{\frac{{b}^{2}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^3+a*x^2)^2,x)
[Out]
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Maxima [A] time = 1.42729, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{2}{7} \, a b x^{7} + \frac{1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193738, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} b^{2} + \frac{2}{7} x^{7} b a + \frac{1}{6} x^{6} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.091962, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**3+a*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217163, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{2}{7} \, a b x^{7} + \frac{1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^2*x,x, algorithm="giac")
[Out]