Optimal. Leaf size=38 \[ -\frac{1}{12 x^3}+\frac{3}{16 x^2}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0267183, antiderivative size = 38, 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 \[ -\frac{1}{12 x^3}+\frac{3}{16 x^2}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(4 + 6*x)),x]
[Out]
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Rubi in Sympy [A] time = 4.38979, size = 34, normalized size = 0.89 \[ - \frac{27 \log{\left (x \right )}}{32} + \frac{27 \log{\left (3 x + 2 \right )}}{32} - \frac{9}{16 x} + \frac{3}{16 x^{2}} - \frac{1}{12 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(4+6*x),x)
[Out]
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Mathematica [A] time = 0.0048551, size = 38, normalized size = 1. \[ -\frac{1}{12 x^3}+\frac{3}{16 x^2}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(4 + 6*x)),x]
[Out]
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Maple [A] time = 0.012, size = 29, normalized size = 0.8 \[ -{\frac{1}{12\,{x}^{3}}}+{\frac{3}{16\,{x}^{2}}}-{\frac{9}{16\,x}}-{\frac{27\,\ln \left ( x \right ) }{32}}+{\frac{27\,\ln \left ( 2+3\,x \right ) }{32}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(4+6*x),x)
[Out]
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Maxima [A] time = 1.38841, size = 38, normalized size = 1. \[ -\frac{27 \, x^{2} - 9 \, x + 4}{48 \, x^{3}} + \frac{27}{32} \, \log \left (3 \, x + 2\right ) - \frac{27}{32} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207803, size = 45, normalized size = 1.18 \[ \frac{81 \, x^{3} \log \left (3 \, x + 2\right ) - 81 \, x^{3} \log \left (x\right ) - 54 \, x^{2} + 18 \, x - 8}{96 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.278805, size = 31, normalized size = 0.82 \[ - \frac{27 \log{\left (x \right )}}{32} + \frac{27 \log{\left (x + \frac{2}{3} \right )}}{32} - \frac{27 x^{2} - 9 x + 4}{48 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(4+6*x),x)
[Out]
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GIAC/XCAS [A] time = 0.205128, size = 41, normalized size = 1.08 \[ -\frac{27 \, x^{2} - 9 \, x + 4}{48 \, x^{3}} + \frac{27}{32} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{27}{32} \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/((3*x + 2)*x^4),x, algorithm="giac")
[Out]