Optimal. Leaf size=39 \[ \frac{1}{32 (3 x+2)}+\frac{1}{32 (3 x+2)^2}+\frac{\log (x)}{64}-\frac{1}{64} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0281361, antiderivative size = 39, 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 \[ \frac{1}{32 (3 x+2)}+\frac{1}{32 (3 x+2)^2}+\frac{\log (x)}{64}-\frac{1}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(4 + 6*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 5.34267, size = 29, normalized size = 0.74 \[ \frac{\log{\left (x \right )}}{64} - \frac{\log{\left (3 x + 2 \right )}}{64} + \frac{1}{32 \left (3 x + 2\right )} + \frac{1}{32 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(4+6*x)**3,x)
[Out]
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Mathematica [A] time = 0.0307152, size = 29, normalized size = 0.74 \[ \frac{1}{64} \left (\frac{6 (x+1)}{(3 x+2)^2}+\log (-6 x)-\log (6 x+4)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(4 + 6*x)^3),x]
[Out]
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Maple [A] time = 0.01, size = 32, normalized size = 0.8 \[{\frac{1}{32\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1}{64+96\,x}}+{\frac{\ln \left ( x \right ) }{64}}-{\frac{\ln \left ( 2+3\,x \right ) }{64}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(4+6*x)^3,x)
[Out]
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Maxima [A] time = 1.32844, size = 41, normalized size = 1.05 \[ \frac{3 \,{\left (x + 1\right )}}{32 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{1}{64} \, \log \left (3 \, x + 2\right ) + \frac{1}{64} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212966, size = 68, normalized size = 1.74 \[ -\frac{{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) -{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (x\right ) - 6 \, x - 6}{64 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.291737, size = 27, normalized size = 0.69 \[ \frac{3 x + 3}{288 x^{2} + 384 x + 128} + \frac{\log{\left (x \right )}}{64} - \frac{\log{\left (x + \frac{2}{3} \right )}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(4+6*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.204996, size = 36, normalized size = 0.92 \[ \frac{3 \,{\left (x + 1\right )}}{32 \,{\left (3 \, x + 2\right )}^{2}} - \frac{1}{64} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1}{64} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x),x, algorithm="giac")
[Out]