Optimal. Leaf size=15 \[ \log (x)-\frac{1}{8} \log \left (1-x^8\right ) \]
[Out]
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Rubi [A] time = 0.0249033, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \log (x)-\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(1 - x^8)),x]
[Out]
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Rubi in Sympy [A] time = 3.94034, size = 14, normalized size = 0.93 \[ \frac{\log{\left (x^{8} \right )}}{8} - \frac{\log{\left (- x^{8} + 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(-x**8+1),x)
[Out]
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Mathematica [A] time = 0.00622879, size = 15, normalized size = 1. \[ \log (x)-\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(1 - x^8)),x]
[Out]
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Maple [B] time = 0.015, size = 32, normalized size = 2.1 \[ \ln \left ( x \right ) -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{\ln \left ({x}^{4}+1 \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(-x^8+1),x)
[Out]
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Maxima [A] time = 1.41509, size = 20, normalized size = 1.33 \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) + \frac{1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213585, size = 15, normalized size = 1. \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.276096, size = 10, normalized size = 0.67 \[ \log{\left (x \right )} - \frac{\log{\left (x^{8} - 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(-x**8+1),x)
[Out]
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GIAC/XCAS [A] time = 0.221763, size = 22, normalized size = 1.47 \[ \frac{1}{8} \,{\rm ln}\left (x^{8}\right ) - \frac{1}{8} \,{\rm ln}\left ({\left | x^{8} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x),x, algorithm="giac")
[Out]