Optimal. Leaf size=25 \[ 4 \left (6-x+4 \left (-2+\frac {x}{16}\right ) x+\log (3 (-3+2 x))\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.60, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {698} \begin {gather*} x^2-36 x+4 \log (3-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-36+2 x+\frac {8}{-3+2 x}\right ) \, dx\\ &=-36 x+x^2+4 \log (3-2 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 0.96 \begin {gather*} 2 \left (\frac {207}{8}-18 x+\frac {x^2}{2}+2 \log (-3+2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 15, normalized size = 0.60 \begin {gather*} x^{2} - 36 \, x + 4 \, \log \left (2 \, x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 16, normalized size = 0.64 \begin {gather*} x^{2} - 36 \, x + 4 \, \log \left ({\left | 2 \, x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 16, normalized size = 0.64
method | result | size |
default | \(-36 x +x^{2}+4 \ln \left (2 x -3\right )\) | \(16\) |
norman | \(-36 x +x^{2}+4 \ln \left (2 x -3\right )\) | \(16\) |
risch | \(-36 x +x^{2}+4 \ln \left (2 x -3\right )\) | \(16\) |
meijerg | \(4 \ln \left (1-\frac {2 x}{3}\right )+\frac {x \left (2 x +6\right )}{2}-39 x\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 15, normalized size = 0.60 \begin {gather*} x^{2} - 36 \, x + 4 \, \log \left (2 \, x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.66, size = 13, normalized size = 0.52 \begin {gather*} 4\,\ln \left (x-\frac {3}{2}\right )-36\,x+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.56 \begin {gather*} x^{2} - 36 x + 4 \log {\left (2 x - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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