Optimal. Leaf size=46 \[ -\frac{1}{64 x}-\frac{3}{32 (3 x+2)}-\frac{3}{64 (3 x+2)^2}-\frac{9 \log (x)}{128}+\frac{9}{128} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0341278, antiderivative size = 46, 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 \[ -\frac{1}{64 x}-\frac{3}{32 (3 x+2)}-\frac{3}{64 (3 x+2)^2}-\frac{9 \log (x)}{128}+\frac{9}{128} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(4 + 6*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 5.48438, size = 37, normalized size = 0.8 \[ - \frac{9 \log{\left (x \right )}}{128} + \frac{9 \log{\left (3 x + 2 \right )}}{128} - \frac{3}{32 \left (3 x + 2\right )} - \frac{3}{64 \left (3 x + 2\right )^{2}} - \frac{1}{64 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(4+6*x)**3,x)
[Out]
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Mathematica [A] time = 0.0381593, size = 39, normalized size = 0.85 \[ \frac{1}{128} \left (-\frac{2 \left (27 x^2+27 x+4\right )}{x (3 x+2)^2}-9 \log (x)+9 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(4 + 6*x)^3),x]
[Out]
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Maple [A] time = 0.016, size = 37, normalized size = 0.8 \[ -{\frac{1}{64\,x}}-{\frac{3}{64\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{3}{64+96\,x}}-{\frac{9\,\ln \left ( x \right ) }{128}}+{\frac{9\,\ln \left ( 2+3\,x \right ) }{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(4+6*x)^3,x)
[Out]
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Maxima [A] time = 1.34845, size = 55, normalized size = 1.2 \[ -\frac{27 \, x^{2} + 27 \, x + 4}{64 \,{\left (9 \, x^{3} + 12 \, x^{2} + 4 \, x\right )}} + \frac{9}{128} \, \log \left (3 \, x + 2\right ) - \frac{9}{128} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214243, size = 92, normalized size = 2. \[ -\frac{54 \, x^{2} - 9 \,{\left (9 \, x^{3} + 12 \, x^{2} + 4 \, x\right )} \log \left (3 \, x + 2\right ) + 9 \,{\left (9 \, x^{3} + 12 \, x^{2} + 4 \, x\right )} \log \left (x\right ) + 54 \, x + 8}{128 \,{\left (9 \, x^{3} + 12 \, x^{2} + 4 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.343376, size = 39, normalized size = 0.85 \[ - \frac{27 x^{2} + 27 x + 4}{576 x^{3} + 768 x^{2} + 256 x} - \frac{9 \log{\left (x \right )}}{128} + \frac{9 \log{\left (x + \frac{2}{3} \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(4+6*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.205316, size = 50, normalized size = 1.09 \[ -\frac{27 \, x^{2} + 27 \, x + 4}{64 \,{\left (3 \, x + 2\right )}^{2} x} + \frac{9}{128} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{9}{128} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/8/((3*x + 2)^3*x^2),x, algorithm="giac")
[Out]