Optimal. Leaf size=54 \[ \frac{a^2 x^6}{6}+\frac{1}{8} x^8 \left (2 a c+b^2\right )+\frac{2}{7} a b x^7+\frac{2}{9} b c x^9+\frac{c^2 x^{10}}{10} \]
[Out]
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Rubi [A] time = 0.0684306, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{a^2 x^6}{6}+\frac{1}{8} x^8 \left (2 a c+b^2\right )+\frac{2}{7} a b x^7+\frac{2}{9} b c x^9+\frac{c^2 x^{10}}{10} \]
Antiderivative was successfully verified.
[In] Int[x*(a*x^2 + b*x^3 + c*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 12.8389, size = 49, normalized size = 0.91 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{7}}{7} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{10}}{10} + x^{8} \left (\frac{a c}{4} + \frac{b^{2}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(c*x**4+b*x**3+a*x**2)**2,x)
[Out]
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Mathematica [A] time = 0.0113031, size = 54, normalized size = 1. \[ \frac{a^2 x^6}{6}+\frac{1}{8} x^8 \left (2 a c+b^2\right )+\frac{2}{7} a b x^7+\frac{2}{9} b c x^9+\frac{c^2 x^{10}}{10} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a*x^2 + b*x^3 + c*x^4)^2,x]
[Out]
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Maple [A] time = 0.002, size = 45, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{6}}{6}}+{\frac{2\,ab{x}^{7}}{7}}+{\frac{ \left ( 2\,ac+{b}^{2} \right ){x}^{8}}{8}}+{\frac{2\,bc{x}^{9}}{9}}+{\frac{{c}^{2}{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(c*x^4+b*x^3+a*x^2)^2,x)
[Out]
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Maxima [A] time = 0.757404, size = 59, normalized size = 1.09 \[ \frac{1}{10} \, c^{2} x^{10} + \frac{2}{9} \, b c x^{9} + \frac{2}{7} \, a b x^{7} + \frac{1}{8} \,{\left (b^{2} + 2 \, a c\right )} x^{8} + \frac{1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242693, size = 1, normalized size = 0.02 \[ \frac{1}{10} x^{10} c^{2} + \frac{2}{9} x^{9} c b + \frac{1}{8} x^{8} b^{2} + \frac{1}{4} x^{8} c a + \frac{2}{7} x^{7} b a + \frac{1}{6} x^{6} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.106732, size = 49, normalized size = 0.91 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{7}}{7} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{10}}{10} + x^{8} \left (\frac{a c}{4} + \frac{b^{2}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(c*x**4+b*x**3+a*x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.260314, size = 62, normalized size = 1.15 \[ \frac{1}{10} \, c^{2} x^{10} + \frac{2}{9} \, b c x^{9} + \frac{1}{8} \, b^{2} x^{8} + \frac{1}{4} \, a c x^{8} + \frac{2}{7} \, a b x^{7} + \frac{1}{6} \, a^{2} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^3 + a*x^2)^2*x,x, algorithm="giac")
[Out]