Optimal. Leaf size=17 \[ \frac{a x^4}{4}+\frac{b x^2}{2} \]
[Out]
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Rubi [A] time = 0.0161627, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^4}{4}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)*x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a x^{4}}{4} + b \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)*x**3,x)
[Out]
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Mathematica [A] time = 0.00180982, size = 17, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)*x^3,x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.8 \[{\frac{b{x}^{2}}{2}}+{\frac{a{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)*x^3,x)
[Out]
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Maxima [A] time = 1.43386, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222844, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.069796, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.226542, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)*x^3,x, algorithm="giac")
[Out]