Optimal. Leaf size=16 \[ \frac{1}{4} \tanh ^{-1}\left (x^4\right )-\frac{1}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0245837, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{1}{4} \tanh ^{-1}\left (x^4\right )-\frac{1}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[1/(x^5*(1 - x^8)),x]
[Out]
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Rubi in Sympy [A] time = 5.37335, size = 12, normalized size = 0.75 \[ \frac{\operatorname{atanh}{\left (x^{4} \right )}}{4} - \frac{1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**5/(-x**8+1),x)
[Out]
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Mathematica [A] time = 0.00719386, size = 30, normalized size = 1.88 \[ -\frac{1}{4 x^4}-\frac{1}{8} \log \left (1-x^4\right )+\frac{1}{8} \log \left (x^4+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^5*(1 - x^8)),x]
[Out]
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Maple [B] time = 0.016, size = 35, normalized size = 2.2 \[ -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{1}{4\,{x}^{4}}}+{\frac{\ln \left ({x}^{4}+1 \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^5/(-x^8+1),x)
[Out]
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Maxima [A] time = 1.44005, size = 30, normalized size = 1.88 \[ -\frac{1}{4 \, x^{4}} + \frac{1}{8} \, \log \left (x^{4} + 1\right ) - \frac{1}{8} \, \log \left (x^{4} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214106, size = 38, normalized size = 2.38 \[ \frac{x^{4} \log \left (x^{4} + 1\right ) - x^{4} \log \left (x^{4} - 1\right ) - 2}{8 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.39724, size = 22, normalized size = 1.38 \[ - \frac{\log{\left (x^{4} - 1 \right )}}{8} + \frac{\log{\left (x^{4} + 1 \right )}}{8} - \frac{1}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**5/(-x**8+1),x)
[Out]
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GIAC/XCAS [A] time = 0.219388, size = 31, normalized size = 1.94 \[ -\frac{1}{4 \, x^{4}} + \frac{1}{8} \,{\rm ln}\left (x^{4} + 1\right ) - \frac{1}{8} \,{\rm ln}\left ({\left | x^{4} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^5),x, algorithm="giac")
[Out]