Optimal. Leaf size=22 \[ -\frac{1}{6 x^6}+\frac{1}{6} \log \left (x^6+1\right )-\log (x) \]
[Out]
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Rubi [A] time = 0.0275422, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{1}{6 x^6}+\frac{1}{6} \log \left (x^6+1\right )-\log (x) \]
Antiderivative was successfully verified.
[In] Int[1/(x^7*(1 + x^6)),x]
[Out]
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Rubi in Sympy [A] time = 3.90876, size = 20, normalized size = 0.91 \[ - \frac{\log{\left (x^{6} \right )}}{6} + \frac{\log{\left (x^{6} + 1 \right )}}{6} - \frac{1}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(x**6+1),x)
[Out]
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Mathematica [A] time = 0.0061104, size = 22, normalized size = 1. \[ -\frac{1}{6 x^6}+\frac{1}{6} \log \left (x^6+1\right )-\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^7*(1 + x^6)),x]
[Out]
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Maple [A] time = 0.012, size = 32, normalized size = 1.5 \[{\frac{\ln \left ({x}^{4}-{x}^{2}+1 \right ) }{6}}-{\frac{1}{6\,{x}^{6}}}-\ln \left ( x \right ) +{\frac{\ln \left ({x}^{2}+1 \right ) }{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(x^6+1),x)
[Out]
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Maxima [A] time = 1.43214, size = 27, normalized size = 1.23 \[ -\frac{1}{6 \, x^{6}} + \frac{1}{6} \, \log \left (x^{6} + 1\right ) - \frac{1}{6} \, \log \left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 1)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211627, size = 32, normalized size = 1.45 \[ \frac{x^{6} \log \left (x^{6} + 1\right ) - 6 \, x^{6} \log \left (x\right ) - 1}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 1)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.389663, size = 17, normalized size = 0.77 \[ - \log{\left (x \right )} + \frac{\log{\left (x^{6} + 1 \right )}}{6} - \frac{1}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(x**6+1),x)
[Out]
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GIAC/XCAS [A] time = 0.229271, size = 34, normalized size = 1.55 \[ \frac{x^{6} - 1}{6 \, x^{6}} + \frac{1}{6} \,{\rm ln}\left (x^{6} + 1\right ) - \frac{1}{6} \,{\rm ln}\left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^6 + 1)*x^7),x, algorithm="giac")
[Out]