Optimal. Leaf size=23 \[ \frac {2 \left (-3+x+\frac {4+x}{9}\right )}{5 (-16+2 x+\log (2))} \]
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Rubi [A] time = 0.02, antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 5, number of rules used = 4, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {12, 1981, 27, 32} \begin {gather*} -\frac {2 (57-\log (32))}{45 (-2 x+16-\log (2))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rule 1981
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((4 (57-\log (32))) \int \frac {1}{11520-2880 x+180 x^2+(-1440+180 x) \log (2)+45 \log ^2(2)} \, dx\right )\\ &=-\left ((4 (57-\log (32))) \int \frac {1}{180 x^2-180 x (16-\log (2))+45 (16-\log (2))^2} \, dx\right )\\ &=-\left ((4 (57-\log (32))) \int \frac {1}{45 (-16+2 x+\log (2))^2} \, dx\right )\\ &=-\left (\frac {1}{45} (4 (57-\log (32))) \int \frac {1}{(-16+2 x+\log (2))^2} \, dx\right )\\ &=-\frac {2 (57-\log (32))}{45 (16-2 x-\log (2))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.74 \begin {gather*} -\frac {2 (-57+\log (32))}{45 (-16+2 x+\log (2))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 17, normalized size = 0.74 \begin {gather*} -\frac {2 \, {\left (5 \, \log \relax (2) - 57\right )}}{45 \, {\left (2 \, x + \log \relax (2) - 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 17, normalized size = 0.74 \begin {gather*} -\frac {2 \, {\left (5 \, \log \relax (2) - 57\right )}}{45 \, {\left (2 \, x + \log \relax (2) - 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 17, normalized size = 0.74
method | result | size |
norman | \(\frac {\frac {38}{15}-\frac {2 \ln \relax (2)}{9}}{\ln \relax (2)+2 x -16}\) | \(17\) |
gosper | \(-\frac {2 \left (5 \ln \relax (2)-57\right )}{45 \left (\ln \relax (2)+2 x -16\right )}\) | \(18\) |
default | \(-\frac {20 \ln \relax (2)-228}{90 \left (\ln \relax (2)+2 x -16\right )}\) | \(18\) |
risch | \(\frac {38}{15 \left (\ln \relax (2)+2 x -16\right )}-\frac {2 \ln \relax (2)}{9 \left (\ln \relax (2)+2 x -16\right )}\) | \(26\) |
meijerg | \(\frac {38 x}{15 \left (\frac {\ln \relax (2)}{2}-8\right ) \left (-\ln \relax (2)+16\right ) \left (1-\frac {2 x}{-\ln \relax (2)+16}\right )}-\frac {2 \ln \relax (2) x}{9 \left (\frac {\ln \relax (2)}{2}-8\right ) \left (-\ln \relax (2)+16\right ) \left (1-\frac {2 x}{-\ln \relax (2)+16}\right )}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 17, normalized size = 0.74 \begin {gather*} -\frac {2 \, {\left (5 \, \log \relax (2) - 57\right )}}{45 \, {\left (2 \, x + \log \relax (2) - 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 17, normalized size = 0.74 \begin {gather*} -\frac {\frac {2\,\ln \relax (2)}{9}-\frac {38}{15}}{2\,x+\ln \relax (2)-16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 0.74 \begin {gather*} - \frac {-228 + 20 \log {\relax (2 )}}{180 x - 1440 + 90 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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