3.2245 \(\int \frac{x}{6-5 x+x^2} \, dx\)

Optimal. Leaf size=17 \[ 3 \log (3-x)-2 \log (2-x) \]

[Out]

-2*Log[2 - x] + 3*Log[3 - x]

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Rubi [A]  time = 0.0194719, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ 3 \log (3-x)-2 \log (2-x) \]

Antiderivative was successfully verified.

[In]  Int[x/(6 - 5*x + x^2),x]

[Out]

-2*Log[2 - x] + 3*Log[3 - x]

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Rubi in Sympy [A]  time = 3.68391, size = 12, normalized size = 0.71 \[ - 2 \log{\left (- x + 2 \right )} + 3 \log{\left (- x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(x**2-5*x+6),x)

[Out]

-2*log(-x + 2) + 3*log(-x + 3)

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Mathematica [A]  time = 0.00633086, size = 17, normalized size = 1. \[ 3 \log (3-x)-2 \log (2-x) \]

Antiderivative was successfully verified.

[In]  Integrate[x/(6 - 5*x + x^2),x]

[Out]

-2*Log[2 - x] + 3*Log[3 - x]

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Maple [A]  time = 0.009, size = 14, normalized size = 0.8 \[ 3\,\ln \left ( x-3 \right ) -2\,\ln \left ( x-2 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(x^2-5*x+6),x)

[Out]

3*ln(x-3)-2*ln(x-2)

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Maxima [A]  time = 0.672277, size = 18, normalized size = 1.06 \[ -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x^2 - 5*x + 6),x, algorithm="maxima")

[Out]

-2*log(x - 2) + 3*log(x - 3)

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Fricas [A]  time = 0.201486, size = 18, normalized size = 1.06 \[ -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x^2 - 5*x + 6),x, algorithm="fricas")

[Out]

-2*log(x - 2) + 3*log(x - 3)

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Sympy [A]  time = 0.183078, size = 12, normalized size = 0.71 \[ 3 \log{\left (x - 3 \right )} - 2 \log{\left (x - 2 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x**2-5*x+6),x)

[Out]

3*log(x - 3) - 2*log(x - 2)

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GIAC/XCAS [A]  time = 0.204702, size = 20, normalized size = 1.18 \[ -2 \,{\rm ln}\left ({\left | x - 2 \right |}\right ) + 3 \,{\rm ln}\left ({\left | x - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x^2 - 5*x + 6),x, algorithm="giac")

[Out]

-2*ln(abs(x - 2)) + 3*ln(abs(x - 3))