Optimal. Leaf size=16 \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
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Rubi [A] time = 0.0212066, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2*x^5,x]
[Out]
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Rubi in Sympy [A] time = 3.4856, size = 10, normalized size = 0.62 \[ \frac{\left (a x^{2} + b\right )^{3}}{6 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2*x**5,x)
[Out]
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Mathematica [A] time = 0.00385963, size = 16, normalized size = 1. \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2*x^5,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 1.6 \[{\frac{{a}^{2}{x}^{6}}{6}}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2*x^5,x)
[Out]
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Maxima [A] time = 1.44141, size = 32, normalized size = 2. \[ \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218408, size = 32, normalized size = 2. \[ \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.088102, size = 24, normalized size = 1.5 \[ \frac{a^{2} x^{6}}{6} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2*x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.226538, size = 32, normalized size = 2. \[ \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^5,x, algorithm="giac")
[Out]