Optimal. Leaf size=39 \[ a^3 \log (x)+\frac{3}{2} a^2 b x^2+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6} \]
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Rubi [A] time = 0.0519704, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ a^3 \log (x)+\frac{3}{2} a^2 b x^2+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} \log{\left (x^{2} \right )}}{2} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} \int ^{x^{2}} x\, dx}{2} + \frac{b^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x,x)
[Out]
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Mathematica [A] time = 0.00654973, size = 39, normalized size = 1. \[ a^3 \log (x)+\frac{3}{2} a^2 b x^2+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x,x]
[Out]
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Maple [A] time = 0.003, size = 34, normalized size = 0.9 \[{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{\frac{3\,a{b}^{2}{x}^{4}}{4}}+{\frac{{b}^{3}{x}^{6}}{6}}+{a}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x,x)
[Out]
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Maxima [A] time = 1.34637, size = 49, normalized size = 1.26 \[ \frac{1}{6} \, b^{3} x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + \frac{1}{2} \, a^{3} \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20157, size = 45, normalized size = 1.15 \[ \frac{1}{6} \, b^{3} x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.05655, size = 37, normalized size = 0.95 \[ a^{3} \log{\left (x \right )} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.209217, size = 49, normalized size = 1.26 \[ \frac{1}{6} \, b^{3} x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + \frac{1}{2} \, a^{3}{\rm ln}\left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x,x, algorithm="giac")
[Out]