Optimal. Leaf size=18 \[ \frac {3}{-\log (6)+\log \left (x+x^2 \log (84)\right )} \]
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Rubi [A] time = 0.25, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {3}{\log (6)-\log (x (x \log (84)+1))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 (-1-2 x \log (84))}{x (1+x \log (84)) (\log (6)-\log (x (1+x \log (84))))^2} \, dx\\ &=3 \int \frac {-1-2 x \log (84)}{x (1+x \log (84)) (\log (6)-\log (x (1+x \log (84))))^2} \, dx\\ &=-\frac {3}{\log (6)-\log (x (1+x \log (84)))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} -\frac {3}{\log (6)-\log (x (1+x \log (84)))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 18, normalized size = 1.00 \begin {gather*} -\frac {3}{\log \relax (6) - \log \left (x^{2} \log \left (84\right ) + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.57, size = 279, normalized size = 15.50 \begin {gather*} -\frac {3 \, {\left (2 \, x^{2} \log \left (84\right ) \log \relax (7) + 2 \, x^{2} \log \left (84\right ) \log \relax (3) + 4 \, x^{2} \log \left (84\right ) \log \relax (2) + x \log \left (84\right ) + 2 \, x \log \relax (7) + 2 \, x \log \relax (3) + 4 \, x \log \relax (2) + 1\right )}}{2 \, x^{2} \log \left (84\right ) \log \relax (7) \log \relax (3) + 2 \, x^{2} \log \left (84\right ) \log \relax (3)^{2} + 2 \, x^{2} \log \left (84\right ) \log \relax (7) \log \relax (2) + 6 \, x^{2} \log \left (84\right ) \log \relax (3) \log \relax (2) + 4 \, x^{2} \log \left (84\right ) \log \relax (2)^{2} - 2 \, x^{2} \log \left (84\right ) \log \relax (7) \log \left (x^{2} \log \left (84\right ) + x\right ) - 2 \, x^{2} \log \left (84\right ) \log \relax (3) \log \left (x^{2} \log \left (84\right ) + x\right ) - 4 \, x^{2} \log \left (84\right ) \log \relax (2) \log \left (x^{2} \log \left (84\right ) + x\right ) + 2 \, x \log \left (84\right ) \log \relax (3) + x \log \relax (7) \log \relax (3) + x \log \relax (3)^{2} + 2 \, x \log \left (84\right ) \log \relax (2) + x \log \relax (7) \log \relax (2) + 3 \, x \log \relax (3) \log \relax (2) + 2 \, x \log \relax (2)^{2} - 2 \, x \log \left (84\right ) \log \left (x^{2} \log \left (84\right ) + x\right ) - x \log \relax (7) \log \left (x^{2} \log \left (84\right ) + x\right ) - x \log \relax (3) \log \left (x^{2} \log \left (84\right ) + x\right ) - 2 \, x \log \relax (2) \log \left (x^{2} \log \left (84\right ) + x\right ) + \log \relax (3) + \log \relax (2) - \log \left (x^{2} \log \left (84\right ) + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 19, normalized size = 1.06
method | result | size |
norman | \(-\frac {3}{\ln \relax (6)-\ln \left (x^{2} \ln \left (84\right )+x \right )}\) | \(19\) |
risch | \(-\frac {3}{\ln \relax (3)+\ln \relax (2)-\ln \left (x^{2} \left (2 \ln \relax (2)+\ln \relax (3)+\ln \relax (7)\right )+x \right )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.84, size = 29, normalized size = 1.61 \begin {gather*} -\frac {3}{\log \relax (3) + \log \relax (2) - \log \left (x {\left (\log \relax (7) + \log \relax (3) + 2 \, \log \relax (2)\right )} + 1\right ) - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.61, size = 16, normalized size = 0.89 \begin {gather*} \frac {3}{\ln \left (\frac {\ln \left (84\right )\,x^2}{6}+\frac {x}{6}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 14, normalized size = 0.78 \begin {gather*} \frac {3}{\log {\left (x^{2} \log {\left (84 \right )} + x \right )} - \log {\relax (6 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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