3.272 \(\int \frac{1}{4-6 x} \, dx\)

Optimal. Leaf size=10 \[ -\frac{1}{6} \log (2-3 x) \]

[Out]

-Log[2 - 3*x]/6

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Rubi [A]  time = 0.00502437, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{6} \log (2-3 x) \]

Antiderivative was successfully verified.

[In]  Int[(4 - 6*x)^(-1),x]

[Out]

-Log[2 - 3*x]/6

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Rubi in Sympy [A]  time = 1.05086, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (- 3 x + 2 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(4-6*x),x)

[Out]

-log(-3*x + 2)/6

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Mathematica [A]  time = 0.00156408, size = 10, normalized size = 1. \[ -\frac{1}{6} \log (4-6 x) \]

Antiderivative was successfully verified.

[In]  Integrate[(4 - 6*x)^(-1),x]

[Out]

-Log[4 - 6*x]/6

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Maple [A]  time = 0.002, size = 9, normalized size = 0.9 \[ -{\frac{\ln \left ( 4-6\,x \right ) }{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(4-6*x),x)

[Out]

-1/6*ln(4-6*x)

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Maxima [A]  time = 1.34124, size = 11, normalized size = 1.1 \[ -\frac{1}{6} \, \log \left (3 \, x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/2/(3*x - 2),x, algorithm="maxima")

[Out]

-1/6*log(3*x - 2)

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Fricas [A]  time = 0.207151, size = 11, normalized size = 1.1 \[ -\frac{1}{6} \, \log \left (3 \, x - 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/2/(3*x - 2),x, algorithm="fricas")

[Out]

-1/6*log(3*x - 2)

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Sympy [A]  time = 0.076162, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (6 x - 4 \right )}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(4-6*x),x)

[Out]

-log(6*x - 4)/6

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GIAC/XCAS [A]  time = 0.209037, size = 12, normalized size = 1.2 \[ -\frac{1}{6} \,{\rm ln}\left ({\left | 3 \, x - 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/2/(3*x - 2),x, algorithm="giac")

[Out]

-1/6*ln(abs(3*x - 2))