Optimal. Leaf size=40 \[ \frac{a^3 x^2}{2}+3 a^2 b \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0626124, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \frac{a^3 x^2}{2}+3 a^2 b \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4} \]
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. \[ \frac{3 a^{2} b \log{\left (x^{2} \right )}}{2} - \frac{3 a b^{2}}{2 x^{2}} - \frac{b^{3}}{4 x^{4}} + \frac{\int ^{x^{2}} a^{3}\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**3*x,x)
[Out]
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Mathematica [A] time = 0.00912048, size = 40, normalized size = 1. \[ \frac{a^3 x^2}{2}+3 a^2 b \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^3*x,x]
[Out]
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Maple [A] time = 0.008, size = 35, normalized size = 0.9 \[ -{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{3\,a{b}^{2}}{2\,{x}^{2}}}+{\frac{{x}^{2}{a}^{3}}{2}}+3\,{a}^{2}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^3*x,x)
[Out]
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Maxima [A] time = 1.44224, size = 50, normalized size = 1.25 \[ \frac{1}{2} \, a^{3} x^{2} + \frac{3}{2} \, a^{2} b \log \left (x^{2}\right ) - \frac{6 \, a b^{2} x^{2} + b^{3}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219988, size = 53, normalized size = 1.32 \[ \frac{2 \, a^{3} x^{6} + 12 \, a^{2} b x^{4} \log \left (x\right ) - 6 \, a b^{2} x^{2} - b^{3}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.35052, size = 36, normalized size = 0.9 \[ \frac{a^{3} x^{2}}{2} + 3 a^{2} b \log{\left (x \right )} - \frac{6 a b^{2} x^{2} + b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**3*x,x)
[Out]
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GIAC/XCAS [A] time = 0.235653, size = 49, normalized size = 1.22 \[ \frac{1}{2} \, a^{3} x^{2} + 3 \, a^{2} b{\rm ln}\left ({\left | x \right |}\right ) - \frac{6 \, a b^{2} x^{2} + b^{3}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x,x, algorithm="giac")
[Out]