Optimal. Leaf size=21 \[ \frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x) \]
[Out]
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Rubi [A] time = 0.0185005, antiderivative size = 21, 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 \[ \frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
[In] Int[(-x^3 + x^4)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.50932, size = 17, normalized size = 0.81 \[ - \log{\left (x \right )} + \log{\left (- x + 1 \right )} + \frac{1}{x} + \frac{1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**4-x**3),x)
[Out]
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Mathematica [A] time = 0.00311023, size = 21, normalized size = 1. \[ \frac{1}{2 x^2}+\frac{1}{x}+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(-x^3 + x^4)^(-1),x]
[Out]
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Maple [A] time = 0.01, size = 18, normalized size = 0.9 \[{\frac{1}{2\,{x}^{2}}}+{x}^{-1}-\ln \left ( x \right ) +\ln \left ( -1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^4-x^3),x)
[Out]
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Maxima [A] time = 1.36104, size = 26, normalized size = 1.24 \[ \frac{2 \, x + 1}{2 \, x^{2}} + \log \left (x - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203377, size = 35, normalized size = 1.67 \[ \frac{2 \, x^{2} \log \left (x - 1\right ) - 2 \, x^{2} \log \left (x\right ) + 2 \, x + 1}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.104677, size = 17, normalized size = 0.81 \[ - \log{\left (x \right )} + \log{\left (x - 1 \right )} + \frac{2 x + 1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**4-x**3),x)
[Out]
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GIAC/XCAS [A] time = 0.221906, size = 28, normalized size = 1.33 \[ \frac{2 \, x + 1}{2 \, x^{2}} +{\rm ln}\left ({\left | x - 1 \right |}\right ) -{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - x^3),x, algorithm="giac")
[Out]