Optimal. Leaf size=42 \[ -\frac{1}{32 x^2}+\frac{3}{16 x}+\frac{9}{32 (3 x+2)}+\frac{27 \log (x)}{64}-\frac{27}{64} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0318018, antiderivative size = 42, 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 \[ -\frac{1}{32 x^2}+\frac{3}{16 x}+\frac{9}{32 (3 x+2)}+\frac{27 \log (x)}{64}-\frac{27}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*(4 + 6*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 5.14411, size = 34, normalized size = 0.81 \[ \frac{27 \log{\left (x \right )}}{64} - \frac{27 \log{\left (3 x + 2 \right )}}{64} + \frac{9}{32 \left (3 x + 2\right )} + \frac{3}{16 x} - \frac{1}{32 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(4+6*x)**2,x)
[Out]
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Mathematica [A] time = 0.0209013, size = 36, normalized size = 0.86 \[ \frac{1}{64} \left (-\frac{2}{x^2}+\frac{12}{x}+\frac{18}{3 x+2}+27 \log (x)-27 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*(4 + 6*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 33, normalized size = 0.8 \[ -{\frac{1}{32\,{x}^{2}}}+{\frac{3}{16\,x}}+{\frac{9}{64+96\,x}}+{\frac{27\,\ln \left ( x \right ) }{64}}-{\frac{27\,\ln \left ( 2+3\,x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(4+6*x)^2,x)
[Out]
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Maxima [A] time = 1.32895, size = 51, normalized size = 1.21 \[ \frac{27 \, x^{2} + 9 \, x - 2}{32 \,{\left (3 \, x^{3} + 2 \, x^{2}\right )}} - \frac{27}{64} \, \log \left (3 \, x + 2\right ) + \frac{27}{64} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210257, size = 80, normalized size = 1.9 \[ \frac{54 \, x^{2} - 27 \,{\left (3 \, x^{3} + 2 \, x^{2}\right )} \log \left (3 \, x + 2\right ) + 27 \,{\left (3 \, x^{3} + 2 \, x^{2}\right )} \log \left (x\right ) + 18 \, x - 4}{64 \,{\left (3 \, x^{3} + 2 \, x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.308357, size = 36, normalized size = 0.86 \[ \frac{27 \log{\left (x \right )}}{64} - \frac{27 \log{\left (x + \frac{2}{3} \right )}}{64} + \frac{27 x^{2} + 9 x - 2}{96 x^{3} + 64 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(4+6*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.203874, size = 69, normalized size = 1.64 \[ \frac{9}{32 \,{\left (3 \, x + 2\right )}} - \frac{9 \,{\left (\frac{12}{3 \, x + 2} - 5\right )}}{128 \,{\left (\frac{2}{3 \, x + 2} - 1\right )}^{2}} + \frac{27}{64} \,{\rm ln}\left ({\left | -\frac{2}{3 \, x + 2} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^3),x, algorithm="giac")
[Out]