Optimal. Leaf size=10 \[ -\frac{1}{3} \tanh ^{-1}\left (x^3+2\right ) \]
[Out]
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Rubi [B] time = 0.0295754, antiderivative size = 21, normalized size of antiderivative = 2.1, number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{1}{6} \log \left (x^3+1\right )-\frac{1}{6} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/(3 + 4*x^3 + x^6),x]
[Out]
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Rubi in Sympy [A] time = 5.73303, size = 15, normalized size = 1.5 \[ \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{\log{\left (x^{3} + 3 \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**6+4*x**3+3),x)
[Out]
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Mathematica [B] time = 0.00635518, size = 21, normalized size = 2.1 \[ \frac{1}{6} \log \left (x^3+1\right )-\frac{1}{6} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(3 + 4*x^3 + x^6),x]
[Out]
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Maple [B] time = 0.007, size = 18, normalized size = 1.8 \[{\frac{\ln \left ({x}^{3}+1 \right ) }{6}}-{\frac{\ln \left ({x}^{3}+3 \right ) }{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^6+4*x^3+3),x)
[Out]
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Maxima [A] time = 0.782302, size = 23, normalized size = 2.3 \[ -\frac{1}{6} \, \log \left (x^{3} + 3\right ) + \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 4*x^3 + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253812, size = 23, normalized size = 2.3 \[ -\frac{1}{6} \, \log \left (x^{3} + 3\right ) + \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 4*x^3 + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.215654, size = 15, normalized size = 1.5 \[ \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{\log{\left (x^{3} + 3 \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**6+4*x**3+3),x)
[Out]
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GIAC/XCAS [A] time = 0.261742, size = 26, normalized size = 2.6 \[ -\frac{1}{6} \,{\rm ln}\left ({\left | x^{3} + 3 \right |}\right ) + \frac{1}{6} \,{\rm ln}\left ({\left | x^{3} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 4*x^3 + 3),x, algorithm="giac")
[Out]