Optimal. Leaf size=12 \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
[Out]
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Rubi [A] time = 0.00751128, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In] Int[x^7/(1 - x^8),x]
[Out]
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Rubi in Sympy [A] time = 2.22334, size = 20, normalized size = 1.67 \[ - \frac{\log{\left (\left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right ) \left (x^{4} + 1\right ) \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(-x**8+1),x)
[Out]
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Mathematica [A] time = 0.00494406, size = 12, normalized size = 1. \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(1 - x^8),x]
[Out]
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Maple [B] time = 0.008, size = 30, normalized size = 2.5 \[ -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}}-{\frac{\ln \left ({x}^{4}+1 \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(-x^8+1),x)
[Out]
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Maxima [A] time = 1.41372, size = 11, normalized size = 0.92 \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^7/(x^8 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209998, size = 11, normalized size = 0.92 \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^7/(x^8 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.238359, size = 8, normalized size = 0.67 \[ - \frac{\log{\left (x^{8} - 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(-x**8+1),x)
[Out]
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GIAC/XCAS [A] time = 0.219962, size = 12, normalized size = 1. \[ -\frac{1}{8} \,{\rm ln}\left ({\left | x^{8} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x^7/(x^8 - 1),x, algorithm="giac")
[Out]