Optimal. Leaf size=17 \[ \frac{\log (x)}{4}-\frac{1}{4} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.010587, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \frac{\log (x)}{4}-\frac{1}{4} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(4 + 6*x)),x]
[Out]
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Rubi in Sympy [A] time = 2.24698, size = 12, normalized size = 0.71 \[ \frac{\log{\left (x \right )}}{4} - \frac{\log{\left (3 x + 2 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(4+6*x),x)
[Out]
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Mathematica [A] time = 0.00380492, size = 17, normalized size = 1. \[ \frac{\log (x)}{4}-\frac{1}{4} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(4 + 6*x)),x]
[Out]
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Maple [A] time = 0., size = 14, normalized size = 0.8 \[{\frac{\ln \left ( x \right ) }{4}}-{\frac{\ln \left ( 2+3\,x \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(4+6*x),x)
[Out]
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Maxima [A] time = 1.34242, size = 18, normalized size = 1.06 \[ -\frac{1}{4} \, \log \left (3 \, x + 2\right ) + \frac{1}{4} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205888, size = 18, normalized size = 1.06 \[ -\frac{1}{4} \, \log \left (3 \, x + 2\right ) + \frac{1}{4} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.187333, size = 12, normalized size = 0.71 \[ \frac{\log{\left (x \right )}}{4} - \frac{\log{\left (x + \frac{2}{3} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(4+6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.202029, size = 20, normalized size = 1.18 \[ -\frac{1}{4} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1}{4} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x),x, algorithm="giac")
[Out]