Optimal. Leaf size=34 \[ -\frac{1}{9 x^3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{1}{54} \log \left (x^3+3\right )-\frac{4 \log (x)}{9} \]
[Out]
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Rubi [A] time = 0.0757246, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ -\frac{1}{9 x^3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{1}{54} \log \left (x^3+3\right )-\frac{4 \log (x)}{9} \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(3 + 4*x^3 + x^6)),x]
[Out]
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Rubi in Sympy [A] time = 16.4955, size = 31, normalized size = 0.91 \[ - \frac{4 \log{\left (x^{3} \right )}}{27} + \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{\log{\left (x^{3} + 3 \right )}}{54} - \frac{1}{9 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(x**6+4*x**3+3),x)
[Out]
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Mathematica [A] time = 0.00963341, size = 34, normalized size = 1. \[ -\frac{1}{9 x^3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{1}{54} \log \left (x^3+3\right )-\frac{4 \log (x)}{9} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(3 + 4*x^3 + x^6)),x]
[Out]
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Maple [A] time = 0.013, size = 36, normalized size = 1.1 \[ -{\frac{\ln \left ({x}^{3}+3 \right ) }{54}}+{\frac{\ln \left ( 1+x \right ) }{6}}-{\frac{1}{9\,{x}^{3}}}-{\frac{4\,\ln \left ( x \right ) }{9}}+{\frac{\ln \left ({x}^{2}-x+1 \right ) }{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(x^6+4*x^3+3),x)
[Out]
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Maxima [A] time = 0.761698, size = 38, normalized size = 1.12 \[ -\frac{1}{9 \, x^{3}} - \frac{1}{54} \, \log \left (x^{3} + 3\right ) + \frac{1}{6} \, \log \left (x^{3} + 1\right ) - \frac{4}{27} \, \log \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 4*x^3 + 3)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253134, size = 47, normalized size = 1.38 \[ -\frac{x^{3} \log \left (x^{3} + 3\right ) - 9 \, x^{3} \log \left (x^{3} + 1\right ) + 24 \, x^{3} \log \left (x\right ) + 6}{54 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 4*x^3 + 3)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.421574, size = 29, normalized size = 0.85 \[ - \frac{4 \log{\left (x \right )}}{9} + \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{\log{\left (x^{3} + 3 \right )}}{54} - \frac{1}{9 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(x**6+4*x**3+3),x)
[Out]
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GIAC/XCAS [A] time = 0.283973, size = 49, normalized size = 1.44 \[ \frac{4 \, x^{3} - 3}{27 \, x^{3}} - \frac{1}{54} \,{\rm ln}\left ({\left | x^{3} + 3 \right |}\right ) + \frac{1}{6} \,{\rm ln}\left ({\left | x^{3} + 1 \right |}\right ) - \frac{4}{9} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 4*x^3 + 3)*x^4),x, algorithm="giac")
[Out]