Optimal. Leaf size=24 \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0216753, antiderivative size = 24, 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 \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(4 + 6*x)),x]
[Out]
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Rubi in Sympy [A] time = 3.58562, size = 20, normalized size = 0.83 \[ - \frac{3 \log{\left (x \right )}}{8} + \frac{3 \log{\left (3 x + 2 \right )}}{8} - \frac{1}{4 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(4+6*x),x)
[Out]
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Mathematica [A] time = 0.00391467, size = 24, normalized size = 1. \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(4 + 6*x)),x]
[Out]
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Maple [A] time = 0.01, size = 19, normalized size = 0.8 \[ -{\frac{1}{4\,x}}-{\frac{3\,\ln \left ( x \right ) }{8}}+{\frac{3\,\ln \left ( 2+3\,x \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(4+6*x),x)
[Out]
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Maxima [A] time = 1.34301, size = 24, normalized size = 1. \[ -\frac{1}{4 \, x} + \frac{3}{8} \, \log \left (3 \, x + 2\right ) - \frac{3}{8} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211774, size = 28, normalized size = 1.17 \[ \frac{3 \, x \log \left (3 \, x + 2\right ) - 3 \, x \log \left (x\right ) - 2}{8 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.210732, size = 20, normalized size = 0.83 \[ - \frac{3 \log{\left (x \right )}}{8} + \frac{3 \log{\left (x + \frac{2}{3} \right )}}{8} - \frac{1}{4 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(4+6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.207361, size = 27, normalized size = 1.12 \[ -\frac{1}{4 \, x} + \frac{3}{8} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{3}{8} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^2),x, algorithm="giac")
[Out]