Optimal. Leaf size=12 \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]
[Out]
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Rubi [A] time = 0.00670748, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
[In] Int[x^3/(2 + 3*x^4),x]
[Out]
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Rubi in Sympy [A] time = 1.9416, size = 8, normalized size = 0.67 \[ \frac{\log{\left (3 x^{4} + 2 \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(3*x**4+2),x)
[Out]
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Mathematica [A] time = 0.0045764, size = 12, normalized size = 1. \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(2 + 3*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \[{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(3*x^4+2),x)
[Out]
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Maxima [A] time = 1.4283, size = 14, normalized size = 1.17 \[ \frac{1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(3*x^4 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2226, size = 14, normalized size = 1.17 \[ \frac{1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(3*x^4 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.144578, size = 8, normalized size = 0.67 \[ \frac{\log{\left (3 x^{4} + 2 \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(3*x**4+2),x)
[Out]
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GIAC/XCAS [A] time = 0.220499, size = 14, normalized size = 1.17 \[ \frac{1}{12} \,{\rm ln}\left (3 \, x^{4} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(3*x^4 + 2),x, algorithm="giac")
[Out]