Optimal. Leaf size=40 \[ \frac{a^3 x^4}{4}+\frac{3}{2} a^2 b x^2+3 a b^2 \log (x)-\frac{b^3}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0692082, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a^3 x^4}{4}+\frac{3}{2} a^2 b x^2+3 a b^2 \log (x)-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^3*x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} \int ^{x^{2}} x\, dx}{2} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} \log{\left (x^{2} \right )}}{2} - \frac{b^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**3*x**3,x)
[Out]
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Mathematica [A] time = 0.012776, size = 40, normalized size = 1. \[ \frac{a^3 x^4}{4}+\frac{3}{2} a^2 b x^2+3 a b^2 \log (x)-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^3*x^3,x]
[Out]
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Maple [A] time = 0.008, size = 35, normalized size = 0.9 \[ -{\frac{{b}^{3}}{2\,{x}^{2}}}+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{\frac{{a}^{3}{x}^{4}}{4}}+3\,a{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^3*x^3,x)
[Out]
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Maxima [A] time = 1.44562, size = 49, normalized size = 1.22 \[ \frac{1}{4} \, a^{3} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + \frac{3}{2} \, a b^{2} \log \left (x^{2}\right ) - \frac{b^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219785, size = 51, normalized size = 1.27 \[ \frac{a^{3} x^{6} + 6 \, a^{2} b x^{4} + 12 \, a b^{2} x^{2} \log \left (x\right ) - 2 \, b^{3}}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.24156, size = 37, normalized size = 0.92 \[ \frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{2}}{2} + 3 a b^{2} \log{\left (x \right )} - \frac{b^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**3*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.22813, size = 47, normalized size = 1.18 \[ \frac{1}{4} \, a^{3} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2}{\rm ln}\left ({\left | x \right |}\right ) - \frac{b^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3*x^3,x, algorithm="giac")
[Out]