Optimal. Leaf size=29 \[ -\frac{1}{4 x^4}-\frac{1}{2 x^2}-\frac{1}{2} \log \left (1-x^2\right )+\log (x) \]
[Out]
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Rubi [A] time = 0.0351831, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{1}{4 x^4}-\frac{1}{2 x^2}-\frac{1}{2} \log \left (1-x^2\right )+\log (x) \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*(x - x^3)),x]
[Out]
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Rubi in Sympy [A] time = 6.10786, size = 27, normalized size = 0.93 \[ \frac{\log{\left (x^{2} \right )}}{2} - \frac{\log{\left (- x^{2} + 1 \right )}}{2} - \frac{1}{2 x^{2}} - \frac{1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(-x**3+x),x)
[Out]
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Mathematica [A] time = 0.00605696, size = 29, normalized size = 1. \[ -\frac{1}{4 x^4}-\frac{1}{2 x^2}-\frac{1}{2} \log \left (1-x^2\right )+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*(x - x^3)),x]
[Out]
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Maple [A] time = 0.013, size = 26, normalized size = 0.9 \[ -{\frac{1}{4\,{x}^{4}}}-{\frac{1}{2\,{x}^{2}}}+\ln \left ( x \right ) -{\frac{\ln \left ( -1+x \right ) }{2}}-{\frac{\ln \left ( 1+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(-x^3+x),x)
[Out]
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Maxima [A] time = 1.38804, size = 36, normalized size = 1.24 \[ -\frac{2 \, x^{2} + 1}{4 \, x^{4}} - \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^3 - x)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202468, size = 41, normalized size = 1.41 \[ -\frac{2 \, x^{4} \log \left (x^{2} - 1\right ) - 4 \, x^{4} \log \left (x\right ) + 2 \, x^{2} + 1}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^3 - x)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.276597, size = 22, normalized size = 0.76 \[ \log{\left (x \right )} - \frac{\log{\left (x^{2} - 1 \right )}}{2} - \frac{2 x^{2} + 1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(-x**3+x),x)
[Out]
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GIAC/XCAS [A] time = 0.220574, size = 45, normalized size = 1.55 \[ -\frac{3 \, x^{4} + 2 \, x^{2} + 1}{4 \, x^{4}} + \frac{1}{2} \,{\rm ln}\left (x^{2}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^3 - x)*x^4),x, algorithm="giac")
[Out]