Optimal. Leaf size=27 \[ \frac {5}{-6+\frac {1}{5} \log (3) (-\log (3)+\log (5+(1+x) (5+x)))} \]
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Rubi [A]
time = 0.15, antiderivative size = 29, normalized size of antiderivative = 1.07, number of steps
used = 4, number of rules used = 3, integrand size = 111, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {12, 6820,
6818} \begin {gather*} -\frac {50 \log (3)}{\log (9) \left (-\log (3) \log \left (x^2+6 x+10\right )+30+\log ^2(3)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \frac {-150-50 x}{9000+5400 x+900 x^2+\left (600+360 x+60 x^2\right ) \log ^2(3)+\left (10+6 x+x^2\right ) \log ^4(3)+\left (\left (-600-360 x-60 x^2\right ) \log (3)+\left (-20-12 x-2 x^2\right ) \log ^3(3)\right ) \log \left (10+6 x+x^2\right )+\left (10+6 x+x^2\right ) \log ^2(3) \log ^2\left (10+6 x+x^2\right )} \, dx\\ &=\log (3) \int \frac {50 (-3-x)}{\left (10+6 x+x^2\right ) \left (30 \left (1+\frac {\log ^2(3)}{30}\right )-\log (3) \log \left (10+6 x+x^2\right )\right )^2} \, dx\\ &=(50 \log (3)) \int \frac {-3-x}{\left (10+6 x+x^2\right ) \left (30 \left (1+\frac {\log ^2(3)}{30}\right )-\log (3) \log \left (10+6 x+x^2\right )\right )^2} \, dx\\ &=-\frac {50 \log (3)}{\log (9) \left (30+\log ^2(3)-\log (3) \log \left (10+6 x+x^2\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 29, normalized size = 1.07 \begin {gather*} -\frac {50 \log (3)}{\log (9) \left (30+\log ^2(3)-\log (3) \log \left (10+6 x+x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.08, size = 25, normalized size = 0.93
method | result | size |
norman | \(-\frac {25}{\ln \left (3\right )^{2}-\ln \left (3\right ) \ln \left (x^{2}+6 x +10\right )+30}\) | \(24\) |
risch | \(-\frac {25}{\ln \left (3\right )^{2}-\ln \left (3\right ) \ln \left (x^{2}+6 x +10\right )+30}\) | \(24\) |
default | \(\frac {25}{-\ln \left (3\right )^{2}+\ln \left (3\right ) \ln \left (x^{2}+6 x +10\right )-30}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 30, normalized size = 1.11 \begin {gather*} -\frac {25 \, \log \left (3\right )}{\log \left (3\right )^{3} - \log \left (3\right )^{2} \log \left (x^{2} + 6 \, x + 10\right ) + 30 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 23, normalized size = 0.85 \begin {gather*} -\frac {25}{\log \left (3\right )^{2} - \log \left (3\right ) \log \left (x^{2} + 6 \, x + 10\right ) + 30} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 20, normalized size = 0.74 \begin {gather*} \frac {25}{\log {\left (3 \right )} \log {\left (x^{2} + 6 x + 10 \right )} - 30 - \log {\left (3 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 30, normalized size = 1.11 \begin {gather*} -\frac {25 \, \log \left (3\right )}{\log \left (3\right )^{3} - \log \left (3\right )^{2} \log \left (x^{2} + 6 \, x + 10\right ) + 30 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.15, size = 30, normalized size = 1.11 \begin {gather*} \frac {25}{\ln \left (3\right )\,\left (\ln \left (x^2+6\,x+10\right )-\frac {{\ln \left (3\right )}^2+30}{\ln \left (3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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