Optimal. Leaf size=39 \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.044821, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[(-18 + 27*x - 7*x^2 - 3*x^3 + x^4)^(-1),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**4-3*x**3-7*x**2+27*x-18),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00952781, size = 39, normalized size = 1. \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(-18 + 27*x - 7*x^2 - 3*x^3 + x^4)^(-1),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.012, size = 26, normalized size = 0.7 \[{\frac{\ln \left ( -1+x \right ) }{8}}+{\frac{\ln \left ( -3+x \right ) }{12}}-{\frac{\ln \left ( x-2 \right ) }{5}}-{\frac{\ln \left ( 3+x \right ) }{120}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^4-3*x^3-7*x^2+27*x-18),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.800236, size = 34, normalized size = 0.87 \[ -\frac{1}{120} \, \log \left (x + 3\right ) + \frac{1}{8} \, \log \left (x - 1\right ) - \frac{1}{5} \, \log \left (x - 2\right ) + \frac{1}{12} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - 3*x^3 - 7*x^2 + 27*x - 18),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.262999, size = 34, normalized size = 0.87 \[ -\frac{1}{120} \, \log \left (x + 3\right ) + \frac{1}{8} \, \log \left (x - 1\right ) - \frac{1}{5} \, \log \left (x - 2\right ) + \frac{1}{12} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - 3*x^3 - 7*x^2 + 27*x - 18),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.654566, size = 26, normalized size = 0.67 \[ \frac{\log{\left (x - 3 \right )}}{12} - \frac{\log{\left (x - 2 \right )}}{5} + \frac{\log{\left (x - 1 \right )}}{8} - \frac{\log{\left (x + 3 \right )}}{120} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**4-3*x**3-7*x**2+27*x-18),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.265846, size = 39, normalized size = 1. \[ -\frac{1}{120} \,{\rm ln}\left ({\left | x + 3 \right |}\right ) + \frac{1}{8} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) - \frac{1}{5} \,{\rm ln}\left ({\left | x - 2 \right |}\right ) + \frac{1}{12} \,{\rm ln}\left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^4 - 3*x^3 - 7*x^2 + 27*x - 18),x, algorithm="giac")
[Out]