Optimal. Leaf size=35 \[ -\frac{1}{16 x}-\frac{3}{16 (3 x+2)}-\frac{3 \log (x)}{16}+\frac{3}{16} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0253209, antiderivative size = 35, 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 \[ -\frac{1}{16 x}-\frac{3}{16 (3 x+2)}-\frac{3 \log (x)}{16}+\frac{3}{16} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(4 + 6*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 4.48447, size = 27, normalized size = 0.77 \[ - \frac{3 \log{\left (x \right )}}{16} + \frac{3 \log{\left (3 x + 2 \right )}}{16} - \frac{3}{16 \left (3 x + 2\right )} - \frac{1}{16 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(4+6*x)**2,x)
[Out]
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Mathematica [A] time = 0.0218254, size = 31, normalized size = 0.89 \[ \frac{1}{16} \left (-\frac{1}{x}-\frac{3}{3 x+2}-3 \log (x)+3 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(4 + 6*x)^2),x]
[Out]
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Maple [A] time = 0.014, size = 28, normalized size = 0.8 \[ -{\frac{1}{16\,x}}-{\frac{3}{32+48\,x}}-{\frac{3\,\ln \left ( x \right ) }{16}}+{\frac{3\,\ln \left ( 2+3\,x \right ) }{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(4+6*x)^2,x)
[Out]
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Maxima [A] time = 1.31772, size = 42, normalized size = 1.2 \[ -\frac{3 \, x + 1}{8 \,{\left (3 \, x^{2} + 2 \, x\right )}} + \frac{3}{16} \, \log \left (3 \, x + 2\right ) - \frac{3}{16} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208669, size = 65, normalized size = 1.86 \[ \frac{3 \,{\left (3 \, x^{2} + 2 \, x\right )} \log \left (3 \, x + 2\right ) - 3 \,{\left (3 \, x^{2} + 2 \, x\right )} \log \left (x\right ) - 6 \, x - 2}{16 \,{\left (3 \, x^{2} + 2 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.264752, size = 29, normalized size = 0.83 \[ - \frac{3 x + 1}{24 x^{2} + 16 x} - \frac{3 \log{\left (x \right )}}{16} + \frac{3 \log{\left (x + \frac{2}{3} \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(4+6*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.2062, size = 54, normalized size = 1.54 \[ -\frac{3}{16 \,{\left (3 \, x + 2\right )}} + \frac{3}{32 \,{\left (\frac{2}{3 \, x + 2} - 1\right )}} - \frac{3}{16} \,{\rm ln}\left ({\left | -\frac{2}{3 \, x + 2} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/4/((3*x + 2)^2*x^2),x, algorithm="giac")
[Out]