Optimal. Leaf size=24 \[ \frac {-2+e^4}{-5+\frac {x \log (4)}{x+\frac {81}{\log ^2(x)}}} \]
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Rubi [A] time = 0.27, antiderivative size = 35, normalized size of antiderivative = 1.46, number of steps used = 3, number of rules used = 4, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6688, 12, 6742, 6686} \begin {gather*} -\frac {81 \left (2-e^4\right ) \log (4)}{(5-\log (4)) \left (x (5-\log (4)) \log ^2(x)+405\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {81 \left (2-e^4\right ) \log (4) \log (x) (2+\log (x))}{\left (405-x (-5+\log (4)) \log ^2(x)\right )^2} \, dx\\ &=\left (81 \left (2-e^4\right ) \log (4)\right ) \int \frac {\log (x) (2+\log (x))}{\left (405-x (-5+\log (4)) \log ^2(x)\right )^2} \, dx\\ &=-\frac {81 \left (2-e^4\right ) \log (4)}{(5-\log (4)) \left (405+x (5-\log (4)) \log ^2(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 1.21 \begin {gather*} \frac {81 \left (-2+e^4\right ) \log (4)}{(-5+\log (4)) \left (-405+x (-5+\log (4)) \log ^2(x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 37, normalized size = 1.54 \begin {gather*} \frac {162 \, {\left (e^{4} - 2\right )} \log \relax (2)}{{\left (4 \, x \log \relax (2)^{2} - 20 \, x \log \relax (2) + 25 \, x\right )} \log \relax (x)^{2} - 810 \, \log \relax (2) + 2025} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.84, size = 47, normalized size = 1.96 \begin {gather*} \frac {162 \, {\left (e^{4} \log \relax (2) - 2 \, \log \relax (2)\right )}}{4 \, x \log \relax (2)^{2} \log \relax (x)^{2} - 20 \, x \log \relax (2) \log \relax (x)^{2} + 25 \, x \log \relax (x)^{2} - 810 \, \log \relax (2) + 2025} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 38, normalized size = 1.58
method | result | size |
norman | \(\frac {\left (\frac {2 \,{\mathrm e}^{4} \ln \relax (2)}{5}-\frac {4 \ln \relax (2)}{5}\right ) x \ln \relax (x )^{2}}{2 \ln \relax (2) \ln \relax (x )^{2} x -5 x \ln \relax (x )^{2}-405}\) | \(38\) |
risch | \(\frac {162 \ln \relax (2) {\mathrm e}^{4}}{\left (2 \ln \relax (2)-5\right ) \left (2 \ln \relax (2) \ln \relax (x )^{2} x -5 x \ln \relax (x )^{2}-405\right )}-\frac {324 \ln \relax (2)}{\left (2 \ln \relax (2)-5\right ) \left (2 \ln \relax (2) \ln \relax (x )^{2} x -5 x \ln \relax (x )^{2}-405\right )}\) | \(68\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 38, normalized size = 1.58 \begin {gather*} \frac {162 \, {\left (e^{4} \log \relax (2) - 2 \, \log \relax (2)\right )}}{{\left (4 \, \log \relax (2)^{2} - 20 \, \log \relax (2) + 25\right )} x \log \relax (x)^{2} - 810 \, \log \relax (2) + 2025} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.11, size = 45, normalized size = 1.88 \begin {gather*} \frac {x^2\,{\ln \relax (x)}^2\,\left (\frac {4\,\ln \relax (2)}{5}-\frac {2\,{\mathrm {e}}^4\,\ln \relax (2)}{5}\right )}{405\,x+5\,x^2\,{\ln \relax (x)}^2-2\,x^2\,\ln \relax (2)\,{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.24, size = 42, normalized size = 1.75 \begin {gather*} \frac {- 324 \log {\relax (2 )} + 162 e^{4} \log {\relax (2 )}}{\left (- 20 x \log {\relax (2 )} + 4 x \log {\relax (2 )}^{2} + 25 x\right ) \log {\relax (x )}^{2} - 810 \log {\relax (2 )} + 2025} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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