Optimal. Leaf size=22 \[ -\frac{1}{8 x^8}-\frac{1}{8} \log \left (1-x^8\right )+\log (x) \]
[Out]
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Rubi [A] time = 0.0320517, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{1}{8 x^8}-\frac{1}{8} \log \left (1-x^8\right )+\log (x) \]
Antiderivative was successfully verified.
[In] Int[1/(x^9*(1 - x^8)),x]
[Out]
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Rubi in Sympy [A] time = 4.95365, size = 20, normalized size = 0.91 \[ \frac{\log{\left (x^{8} \right )}}{8} - \frac{\log{\left (- x^{8} + 1 \right )}}{8} - \frac{1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**9/(-x**8+1),x)
[Out]
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Mathematica [A] time = 0.00660765, size = 22, normalized size = 1. \[ -\frac{1}{8 x^8}-\frac{1}{8} \log \left (1-x^8\right )+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^9*(1 - x^8)),x]
[Out]
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Maple [A] time = 0.018, size = 37, normalized size = 1.7 \[ -{\frac{1}{8\,{x}^{8}}}+\ln \left ( x \right ) -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{\ln \left ({x}^{4}+1 \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^9/(-x^8+1),x)
[Out]
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Maxima [A] time = 1.43906, size = 27, normalized size = 1.23 \[ -\frac{1}{8 \, x^{8}} - \frac{1}{8} \, \log \left (x^{8} - 1\right ) + \frac{1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214903, size = 32, normalized size = 1.45 \[ -\frac{x^{8} \log \left (x^{8} - 1\right ) - 8 \, x^{8} \log \left (x\right ) + 1}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.543971, size = 17, normalized size = 0.77 \[ \log{\left (x \right )} - \frac{\log{\left (x^{8} - 1 \right )}}{8} - \frac{1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**9/(-x**8+1),x)
[Out]
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GIAC/XCAS [A] time = 0.2184, size = 35, normalized size = 1.59 \[ -\frac{x^{8} + 1}{8 \, x^{8}} + \frac{1}{8} \,{\rm ln}\left (x^{8}\right ) - \frac{1}{8} \,{\rm ln}\left ({\left | x^{8} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((x^8 - 1)*x^9),x, algorithm="giac")
[Out]