Optimal. Leaf size=22 \[ \frac{1}{3} \log \left (x^2+x+1\right )-\frac{2}{3} \log (1-x) \]
[Out]
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Rubi [A] time = 0.0226266, antiderivative size = 22, 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 \[ \frac{1}{3} \log \left (x^2+x+1\right )-\frac{2}{3} \log (1-x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x)/(1 - x^3),x]
[Out]
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Rubi in Sympy [A] time = 6.72534, size = 17, normalized size = 0.77 \[ - \frac{2 \log{\left (- x + 1 \right )}}{3} + \frac{\log{\left (x^{2} + x + 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)/(-x**3+1),x)
[Out]
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Mathematica [A] time = 0.00754296, size = 22, normalized size = 1. \[ \frac{1}{3} \log \left (x^2+x+1\right )-\frac{2}{3} \log (1-x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)/(1 - x^3),x]
[Out]
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Maple [A] time = 0.007, size = 17, normalized size = 0.8 \[{\frac{\ln \left ({x}^{2}+x+1 \right ) }{3}}-{\frac{2\,\ln \left ( -1+x \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)/(-x^3+1),x)
[Out]
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Maxima [A] time = 1.51777, size = 22, normalized size = 1. \[ \frac{1}{3} \, \log \left (x^{2} + x + 1\right ) - \frac{2}{3} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x + 1)/(x^3 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207835, size = 22, normalized size = 1. \[ \frac{1}{3} \, \log \left (x^{2} + x + 1\right ) - \frac{2}{3} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x + 1)/(x^3 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.095287, size = 17, normalized size = 0.77 \[ - \frac{2 \log{\left (x - 1 \right )}}{3} + \frac{\log{\left (x^{2} + x + 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)/(-x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.209055, size = 23, normalized size = 1.05 \[ \frac{1}{3} \,{\rm ln}\left (x^{2} + x + 1\right ) - \frac{2}{3} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x + 1)/(x^3 - 1),x, algorithm="giac")
[Out]