3.265 \(\int \frac{1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx\)

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]

Log[1 - x]/8 - Log[2 - x]/5 + Log[3 - x]/12 - Log[3 + x]/120

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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]

Log[1 - x]/8 - Log[2 - x]/5 + Log[3 - x]/12 - Log[3 + x]/120

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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]

Timed out

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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]

Log[1 - x]/8 - Log[2 - x]/5 + Log[3 - x]/12 - Log[3 + x]/120

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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]

1/8*ln(-1+x)+1/12*ln(-3+x)-1/5*ln(x-2)-1/120*ln(3+x)

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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]

-1/120*log(x + 3) + 1/8*log(x - 1) - 1/5*log(x - 2) + 1/12*log(x - 3)

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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]

-1/120*log(x + 3) + 1/8*log(x - 1) - 1/5*log(x - 2) + 1/12*log(x - 3)

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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]

log(x - 3)/12 - log(x - 2)/5 + log(x - 1)/8 - log(x + 3)/120

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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]

-1/120*ln(abs(x + 3)) + 1/8*ln(abs(x - 1)) - 1/5*ln(abs(x - 2)) + 1/12*ln(abs(x
- 3))