Optimal. Leaf size=12 \[ \frac{4}{1-x}+\tanh ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.0402657, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{4}{1-x}+\tanh ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[(5 + 3*x)/(1 - x - x^2 + x^3),x]
[Out]
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Rubi in Sympy [A] time = 15.4377, size = 7, normalized size = 0.58 \[ \operatorname{atanh}{\left (x \right )} + \frac{4}{- x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5+3*x)/(x**3-x**2-x+1),x)
[Out]
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Mathematica [A] time = 0.0158097, size = 24, normalized size = 2. \[ -\frac{4}{x-1}-\frac{1}{2} \log (x-1)+\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(5 + 3*x)/(1 - x - x^2 + x^3),x]
[Out]
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Maple [A] time = 0.011, size = 21, normalized size = 1.8 \[ -4\, \left ( -1+x \right ) ^{-1}-{\frac{\ln \left ( -1+x \right ) }{2}}+{\frac{\ln \left ( 1+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5+3*x)/(x^3-x^2-x+1),x)
[Out]
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Maxima [A] time = 0.789688, size = 27, normalized size = 2.25 \[ -\frac{4}{x - 1} + \frac{1}{2} \, \log \left (x + 1\right ) - \frac{1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 5)/(x^3 - x^2 - x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248448, size = 35, normalized size = 2.92 \[ \frac{{\left (x - 1\right )} \log \left (x + 1\right ) -{\left (x - 1\right )} \log \left (x - 1\right ) - 8}{2 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 5)/(x^3 - x^2 - x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.186911, size = 17, normalized size = 1.42 \[ - \frac{\log{\left (x - 1 \right )}}{2} + \frac{\log{\left (x + 1 \right )}}{2} - \frac{4}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5+3*x)/(x**3-x**2-x+1),x)
[Out]
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GIAC/XCAS [A] time = 0.264683, size = 30, normalized size = 2.5 \[ -\frac{4}{x - 1} + \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) - \frac{1}{2} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 5)/(x^3 - x^2 - x + 1),x, algorithm="giac")
[Out]