Optimal. Leaf size=19 \[ \frac {2}{16-\log (x)+\log \left (3+\frac {3}{\log (x)}\right )} \]
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Rubi [A] time = 0.22, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 4, number of rules used = 3, integrand size = 100, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {12, 1593, 6686} \begin {gather*} \frac {2}{-\log (x)+\log \left (\frac {3 (\log (x)+1)}{\log (x)}\right )+16} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {2 \left (1+x+x^2\right )}{\left (x+x^2\right ) \left (-16+x-\log \left (\frac {3+3 x}{x}\right )\right )^2} \, dx,x,\log (x)\right )\\ &=2 \operatorname {Subst}\left (\int \frac {1+x+x^2}{\left (x+x^2\right ) \left (-16+x-\log \left (\frac {3+3 x}{x}\right )\right )^2} \, dx,x,\log (x)\right )\\ &=2 \operatorname {Subst}\left (\int \frac {1+x+x^2}{x (1+x) \left (-16+x-\log \left (\frac {3+3 x}{x}\right )\right )^2} \, dx,x,\log (x)\right )\\ &=\frac {2}{16-\log (x)+\log \left (\frac {3 (1+\log (x))}{\log (x)}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 19, normalized size = 1.00 \begin {gather*} \frac {2}{16-\log (x)+\log \left (3+\frac {3}{\log (x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 21, normalized size = 1.11 \begin {gather*} -\frac {2}{\log \relax (x) - \log \left (\frac {3 \, {\left (\log \relax (x) + 1\right )}}{\log \relax (x)}\right ) - 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.28, size = 60, normalized size = 3.16 \begin {gather*} \frac {2 \, {\left (\frac {\log \relax (x) + 1}{\log \relax (x)} - 1\right )}}{\frac {{\left (\log \relax (x) + 1\right )} \log \left (\frac {3 \, {\left (\log \relax (x) + 1\right )}}{\log \relax (x)}\right )}{\log \relax (x)} + \frac {16 \, {\left (\log \relax (x) + 1\right )}}{\log \relax (x)} - \log \left (\frac {3 \, {\left (\log \relax (x) + 1\right )}}{\log \relax (x)}\right ) - 17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.24, size = 129, normalized size = 6.79
method | result | size |
risch | \(\frac {4 i}{\pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )+1\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+1\right )}{\ln \relax (x )}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+1\right )}{\ln \relax (x )}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )+1\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+1\right )}{\ln \relax (x )}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+1\right )}{\ln \relax (x )}\right )^{3}+2 i \ln \relax (3)-2 i \ln \relax (x )-2 i \ln \left (\ln \relax (x )\right )+2 i \ln \left (\ln \relax (x )+1\right )+32 i}\) | \(129\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.86, size = 22, normalized size = 1.16 \begin {gather*} \frac {2}{\log \relax (3) - \log \relax (x) + \log \left (\log \relax (x) + 1\right ) - \log \left (\log \relax (x)\right ) + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.00, size = 22, normalized size = 1.16 \begin {gather*} \frac {2}{\ln \left (\frac {3\,\ln \relax (x)+3}{\ln \relax (x)}\right )-\ln \relax (x)+16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 17, normalized size = 0.89 \begin {gather*} \frac {2}{- \log {\relax (x )} + \log {\left (\frac {3 \log {\relax (x )} + 3}{\log {\relax (x )}} \right )} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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