Optimal. Leaf size=45 \[ -\frac{1}{16 x^4}+\frac{1}{8 x^3}-\frac{9}{32 x^2}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.03064, antiderivative size = 45, 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 \[ -\frac{1}{16 x^4}+\frac{1}{8 x^3}-\frac{9}{32 x^2}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(4 + 6*x)),x]
[Out]
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Rubi in Sympy [A] time = 4.85974, size = 41, normalized size = 0.91 \[ \frac{81 \log{\left (x \right )}}{64} - \frac{81 \log{\left (3 x + 2 \right )}}{64} + \frac{27}{32 x} - \frac{9}{32 x^{2}} + \frac{1}{8 x^{3}} - \frac{1}{16 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(4+6*x),x)
[Out]
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Mathematica [A] time = 0.00414986, size = 45, normalized size = 1. \[ -\frac{1}{16 x^4}+\frac{1}{8 x^3}-\frac{9}{32 x^2}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(4 + 6*x)),x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 0.8 \[ -{\frac{1}{16\,{x}^{4}}}+{\frac{1}{8\,{x}^{3}}}-{\frac{9}{32\,{x}^{2}}}+{\frac{27}{32\,x}}+{\frac{81\,\ln \left ( x \right ) }{64}}-{\frac{81\,\ln \left ( 2+3\,x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(4+6*x),x)
[Out]
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Maxima [A] time = 1.34691, size = 45, normalized size = 1. \[ \frac{27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac{81}{64} \, \log \left (3 \, x + 2\right ) + \frac{81}{64} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212699, size = 51, normalized size = 1.13 \[ -\frac{81 \, x^{4} \log \left (3 \, x + 2\right ) - 81 \, x^{4} \log \left (x\right ) - 54 \, x^{3} + 18 \, x^{2} - 8 \, x + 4}{64 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.298061, size = 36, normalized size = 0.8 \[ \frac{81 \log{\left (x \right )}}{64} - \frac{81 \log{\left (x + \frac{2}{3} \right )}}{64} + \frac{27 x^{3} - 9 x^{2} + 4 x - 2}{32 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(4+6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.203864, size = 47, normalized size = 1.04 \[ \frac{27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac{81}{64} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{81}{64} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^5),x, algorithm="giac")
[Out]