Optimal. Leaf size=31 \[ -\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0238058, antiderivative size = 31, 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 \[ -\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(4 + 6*x)),x]
[Out]
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Rubi in Sympy [A] time = 4.08248, size = 27, normalized size = 0.87 \[ \frac{9 \log{\left (x \right )}}{16} - \frac{9 \log{\left (3 x + 2 \right )}}{16} + \frac{3}{8 x} - \frac{1}{8 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(4+6*x),x)
[Out]
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Mathematica [A] time = 0.00393771, size = 31, normalized size = 1. \[ -\frac{1}{8 x^2}+\frac{3}{8 x}+\frac{9 \log (x)}{16}-\frac{9}{16} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(4 + 6*x)),x]
[Out]
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Maple [A] time = 0.011, size = 24, normalized size = 0.8 \[ -{\frac{1}{8\,{x}^{2}}}+{\frac{3}{8\,x}}+{\frac{9\,\ln \left ( x \right ) }{16}}-{\frac{9\,\ln \left ( 2+3\,x \right ) }{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(4+6*x),x)
[Out]
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Maxima [A] time = 1.33352, size = 31, normalized size = 1. \[ \frac{3 \, x - 1}{8 \, x^{2}} - \frac{9}{16} \, \log \left (3 \, x + 2\right ) + \frac{9}{16} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206109, size = 38, normalized size = 1.23 \[ -\frac{9 \, x^{2} \log \left (3 \, x + 2\right ) - 9 \, x^{2} \log \left (x\right ) - 6 \, x + 2}{16 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.243409, size = 26, normalized size = 0.84 \[ \frac{9 \log{\left (x \right )}}{16} - \frac{9 \log{\left (x + \frac{2}{3} \right )}}{16} + \frac{3 x - 1}{8 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(4+6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.204247, size = 34, normalized size = 1.1 \[ \frac{3 \, x - 1}{8 \, x^{2}} - \frac{9}{16} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{9}{16} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^3),x, algorithm="giac")
[Out]