Optimal. Leaf size=20 \[ 2 x+\frac {12 x}{-9+x+\log \left (-4+\frac {x}{3}\right )} \]
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Rubi [F]
time = 0.63, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-648+474 x-60 x^2+2 x^3+\left (288-72 x+4 x^2\right ) \log \left (\frac {1}{3} (-12+x)\right )+(-24+2 x) \log ^2\left (\frac {1}{3} (-12+x)\right )}{-972+297 x-30 x^2+x^3+\left (216-42 x+2 x^2\right ) \log \left (\frac {1}{3} (-12+x)\right )+(-12+x) \log ^2\left (\frac {1}{3} (-12+x)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (324-237 x+30 x^2-x^3-2 \left (72-18 x+x^2\right ) \log \left (-4+\frac {x}{3}\right )-(-12+x) \log ^2\left (-4+\frac {x}{3}\right )\right )}{(12-x) \left (9-x-\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx\\ &=2 \int \frac {324-237 x+30 x^2-x^3-2 \left (72-18 x+x^2\right ) \log \left (-4+\frac {x}{3}\right )-(-12+x) \log ^2\left (-4+\frac {x}{3}\right )}{(12-x) \left (9-x-\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx\\ &=2 \int \left (1-\frac {6 (-11+x) x}{(-12+x) \left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2}+\frac {6}{-9+x+\log \left (-4+\frac {x}{3}\right )}\right ) \, dx\\ &=2 x-12 \int \frac {(-11+x) x}{(-12+x) \left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx+12 \int \frac {1}{-9+x+\log \left (-4+\frac {x}{3}\right )} \, dx\\ &=2 x+12 \int \frac {1}{-9+x+\log \left (-4+\frac {x}{3}\right )} \, dx-12 \int \left (\frac {1}{\left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2}+\frac {12}{(-12+x) \left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2}+\frac {x}{\left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2}\right ) \, dx\\ &=2 x-12 \int \frac {1}{\left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx-12 \int \frac {x}{\left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx+12 \int \frac {1}{-9+x+\log \left (-4+\frac {x}{3}\right )} \, dx-144 \int \frac {1}{(-12+x) \left (-9+x+\log \left (-4+\frac {x}{3}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 20, normalized size = 1.00 \begin {gather*} 2 \left (x+\frac {6 x}{-9+x+\log \left (-4+\frac {x}{3}\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(39\) vs.
\(2(18)=36\).
time = 9.22, size = 40, normalized size = 2.00
method | result | size |
risch | \(2 x +\frac {12 x}{\ln \left (\frac {x}{3}-4\right )-9+x}\) | \(19\) |
derivativedivides | \(\frac {6 \ln \left (\frac {x}{3}-4\right ) \left (\frac {x}{3}-4\right )+18 x -72+18 \left (\frac {x}{3}-4\right )^{2}}{\ln \left (\frac {x}{3}-4\right )-9+x}\) | \(40\) |
default | \(\frac {6 \ln \left (\frac {x}{3}-4\right ) \left (\frac {x}{3}-4\right )+18 x -72+18 \left (\frac {x}{3}-4\right )^{2}}{\ln \left (\frac {x}{3}-4\right )-9+x}\) | \(40\) |
norman | \(\frac {-2 \ln \left (\frac {x}{3}-4\right )^{2}+24 \ln \left (\frac {x}{3}-4\right )+2 x^{2}-54}{\ln \left (\frac {x}{3}-4\right )-9+x}+2 \ln \left (x -12\right )\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 32, normalized size = 1.60 \begin {gather*} \frac {2 \, {\left (x^{2} - x {\left (\log \left (3\right ) + 3\right )} + x \log \left (x - 12\right )\right )}}{x - \log \left (3\right ) + \log \left (x - 12\right ) - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.40 \begin {gather*} \frac {2 \, {\left (x^{2} + x \log \left (\frac {1}{3} \, x - 4\right ) - 3 \, x\right )}}{x + \log \left (\frac {1}{3} \, x - 4\right ) - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.75 \begin {gather*} 2 x + \frac {12 x}{x + \log {\left (\frac {x}{3} - 4 \right )} - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 18, normalized size = 0.90 \begin {gather*} 2 \, x + \frac {12 \, x}{x + \log \left (\frac {1}{3} \, x - 4\right ) - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.59, size = 37, normalized size = 1.85 \begin {gather*} \frac {2\,\left (x\,\ln \left (\frac {x}{3}-4\right )-6\,\ln \left (\frac {x}{3}-4\right )-9\,x+x^2+54\right )}{x+\ln \left (\frac {x}{3}-4\right )-9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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