Optimal. Leaf size=32 \[ \frac{1}{3} (a-c) \log \left (x^2+x+1\right )-\frac{1}{3} (2 a+c) \log (1-x) \]
[Out]
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Rubi [A] time = 0.060001, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ \frac{1}{3} (a-c) \log \left (x^2+x+1\right )-\frac{1}{3} (2 a+c) \log (1-x) \]
Antiderivative was successfully verified.
[In] Int[(a + a*x + c*x^2)/(1 - x^3),x]
[Out]
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Rubi in Sympy [A] time = 11.8263, size = 27, normalized size = 0.84 \[ \left (\frac{a}{3} - \frac{c}{3}\right ) \log{\left (x^{2} + x + 1 \right )} - \left (\frac{2 a}{3} + \frac{c}{3}\right ) \log{\left (- x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+a*x+a)/(-x**3+1),x)
[Out]
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Mathematica [A] time = 0.0234506, size = 31, normalized size = 0.97 \[ \frac{1}{3} \left ((a-c) \log \left (x^2+x+1\right )-(2 a+c) \log (1-x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + a*x + c*x^2)/(1 - x^3),x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 1.1 \[{\frac{\ln \left ({x}^{2}+x+1 \right ) a}{3}}-{\frac{\ln \left ({x}^{2}+x+1 \right ) c}{3}}-{\frac{\ln \left ( -1+x \right ) c}{3}}-{\frac{2\,\ln \left ( -1+x \right ) a}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+a*x+a)/(-x^3+1),x)
[Out]
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Maxima [A] time = 1.57875, size = 35, normalized size = 1.09 \[ \frac{1}{3} \,{\left (a - c\right )} \log \left (x^{2} + x + 1\right ) - \frac{1}{3} \,{\left (2 \, a + c\right )} \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(c*x^2 + a*x + a)/(x^3 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21926, size = 35, normalized size = 1.09 \[ \frac{1}{3} \,{\left (a - c\right )} \log \left (x^{2} + x + 1\right ) - \frac{1}{3} \,{\left (2 \, a + c\right )} \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(c*x^2 + a*x + a)/(x^3 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.496307, size = 24, normalized size = 0.75 \[ \frac{\left (a - c\right ) \log{\left (x^{2} + x + 1 \right )}}{3} - \frac{\left (2 a + c\right ) \log{\left (x - 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+a*x+a)/(-x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.219611, size = 36, normalized size = 1.12 \[ \frac{1}{3} \,{\left (a - c\right )}{\rm ln}\left (x^{2} + x + 1\right ) - \frac{1}{3} \,{\left (2 \, a + c\right )}{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(c*x^2 + a*x + a)/(x^3 - 1),x, algorithm="giac")
[Out]