3.259 \(\int \frac{-9-9 x+2 x^2}{-9 x+x^3} \, dx\)

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

[Out]

-Log[3 - x] + Log[x] + 2*Log[3 + x]

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Rubi [A]  time = 0.0526702, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\log (3-x)+\log (x)+2 \log (x+3) \]

Antiderivative was successfully verified.

[In]  Int[(-9 - 9*x + 2*x^2)/(-9*x + x^3),x]

[Out]

-Log[3 - x] + Log[x] + 2*Log[3 + x]

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Rubi in Sympy [A]  time = 9.1575, size = 14, normalized size = 0.82 \[ \log{\left (x \right )} - \log{\left (- x + 3 \right )} + 2 \log{\left (x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2*x**2-9*x-9)/(x**3-9*x),x)

[Out]

log(x) - log(-x + 3) + 2*log(x + 3)

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Mathematica [A]  time = 0.00906288, size = 17, normalized size = 1. \[ -\log (3-x)+\log (x)+2 \log (x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(-9 - 9*x + 2*x^2)/(-9*x + x^3),x]

[Out]

-Log[3 - x] + Log[x] + 2*Log[3 + x]

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Maple [A]  time = 0.011, size = 16, normalized size = 0.9 \[ -\ln \left ( -3+x \right ) +\ln \left ( x \right ) +2\,\ln \left ( 3+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2*x^2-9*x-9)/(x^3-9*x),x)

[Out]

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

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Maxima [A]  time = 0.996735, size = 20, normalized size = 1.18 \[ 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="maxima")

[Out]

2*log(x + 3) - log(x - 3) + log(x)

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Fricas [A]  time = 0.258079, size = 20, normalized size = 1.18 \[ 2 \, \log \left (x + 3\right ) - \log \left (x - 3\right ) + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="fricas")

[Out]

2*log(x + 3) - log(x - 3) + log(x)

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Sympy [A]  time = 0.270863, size = 14, normalized size = 0.82 \[ \log{\left (x \right )} - \log{\left (x - 3 \right )} + 2 \log{\left (x + 3 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x**2-9*x-9)/(x**3-9*x),x)

[Out]

log(x) - log(x - 3) + 2*log(x + 3)

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GIAC/XCAS [A]  time = 0.262644, size = 24, normalized size = 1.41 \[ 2 \,{\rm ln}\left ({\left | x + 3 \right |}\right ) -{\rm ln}\left ({\left | x - 3 \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x^2 - 9*x - 9)/(x^3 - 9*x),x, algorithm="giac")

[Out]

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