Optimal. Leaf size=25 \[ \frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x) \]
[Out]
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Rubi [A] time = 0.0257369, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2}{1-x}-\frac{1}{(1-x)^2}+\log (1-x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^2)/(-1 + x)^3,x]
[Out]
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Rubi in Sympy [A] time = 1.88216, size = 15, normalized size = 0.6 \[ \log{\left (- x + 1 \right )} + \frac{2}{- x + 1} - \frac{1}{\left (- x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+1)/(-1+x)**3,x)
[Out]
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Mathematica [A] time = 0.014837, size = 16, normalized size = 0.64 \[ \frac{1-2 x}{(x-1)^2}+\log (x-1) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^2)/(-1 + x)^3,x]
[Out]
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Maple [A] time = 0.009, size = 20, normalized size = 0.8 \[ - \left ( -1+x \right ) ^{-2}+\ln \left ( -1+x \right ) -2\, \left ( -1+x \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+1)/(-1+x)^3,x)
[Out]
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Maxima [A] time = 1.35041, size = 30, normalized size = 1.2 \[ -\frac{2 \, x - 1}{x^{2} - 2 \, x + 1} + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201252, size = 39, normalized size = 1.56 \[ \frac{{\left (x^{2} - 2 \, x + 1\right )} \log \left (x - 1\right ) - 2 \, x + 1}{x^{2} - 2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.09555, size = 17, normalized size = 0.68 \[ - \frac{2 x - 1}{x^{2} - 2 x + 1} + \log{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+1)/(-1+x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.200817, size = 24, normalized size = 0.96 \[ -\frac{2 \, x - 1}{{\left (x - 1\right )}^{2}} +{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x - 1)^3,x, algorithm="giac")
[Out]