Optimal. Leaf size=26 \[ \frac {12}{-25-\log (4)+3^{-1/x} \sqrt [x]{\log \left (x^4\right )}} \]
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Rubi [A] time = 1.58, antiderivative size = 33, normalized size of antiderivative = 1.27, number of steps used = 4, number of rules used = 4, integrand size = 116, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6688, 12, 6711, 32} \begin {gather*} \frac {12}{(25+\log (4)) \left (1-3^{\frac {1}{x}} (25+\log (4)) \log ^{-\frac {1}{x}}\left (x^4\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rule 6688
Rule 6711
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4\ 3^{1+\frac {1}{x}} \log ^{-1+\frac {1}{x}}\left (x^4\right ) \left (-4+\log \left (x^4\right ) \log \left (\frac {\log \left (x^4\right )}{3}\right )\right )}{x^2 \left (3^{\frac {1}{x}} (25+\log (4))-\sqrt [x]{\log \left (x^4\right )}\right )^2} \, dx\\ &=4 \int \frac {3^{1+\frac {1}{x}} \log ^{-1+\frac {1}{x}}\left (x^4\right ) \left (-4+\log \left (x^4\right ) \log \left (\frac {\log \left (x^4\right )}{3}\right )\right )}{x^2 \left (3^{\frac {1}{x}} (25+\log (4))-\sqrt [x]{\log \left (x^4\right )}\right )^2} \, dx\\ &=12 \operatorname {Subst}\left (\int \frac {1}{(-1+x (25+\log (4)))^2} \, dx,x,3^{\frac {1}{x}} \log ^{-\frac {1}{x}}\left (x^4\right )\right )\\ &=\frac {12}{(25+\log (4)) \left (1-3^{\frac {1}{x}} (25+\log (4)) \log ^{-\frac {1}{x}}\left (x^4\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.60, size = 32, normalized size = 1.23 \begin {gather*} -\frac {4\ 3^{1+\frac {1}{x}}}{3^{\frac {1}{x}} (25+\log (4))-\sqrt [x]{\log \left (x^4\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 20, normalized size = 0.77 \begin {gather*} \frac {12}{\left (\frac {1}{3} \, \log \left (x^{4}\right )\right )^{\left (\frac {1}{x}\right )} - 2 \, \log \relax (2) - 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {12 \, {\left (\log \left (x^{4}\right ) \log \left (\frac {1}{3} \, \log \left (x^{4}\right )\right ) - 4\right )} \left (\frac {1}{3} \, \log \left (x^{4}\right )\right )^{\left (\frac {1}{x}\right )}}{x^{2} \left (\frac {1}{3} \, \log \left (x^{4}\right )\right )^{\frac {2}{x}} \log \left (x^{4}\right ) - 2 \, {\left (2 \, x^{2} \log \relax (2) + 25 \, x^{2}\right )} \left (\frac {1}{3} \, \log \left (x^{4}\right )\right )^{\left (\frac {1}{x}\right )} \log \left (x^{4}\right ) + {\left (4 \, x^{2} \log \relax (2)^{2} + 100 \, x^{2} \log \relax (2) + 625 \, x^{2}\right )} \log \left (x^{4}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.23, size = 0, normalized size = 0.00 \[\int \frac {\left (12 \ln \left (x^{4}\right ) \ln \left (\frac {\ln \left (x^{4}\right )}{3}\right )-48\right ) {\mathrm e}^{\frac {\ln \left (\frac {\ln \left (x^{4}\right )}{3}\right )}{x}}}{x^{2} \ln \left (x^{4}\right ) {\mathrm e}^{\frac {2 \ln \left (\ln \left (\left (x^{4}\right )^{\frac {1}{3}}\right )\right )}{x}}+\left (-4 x^{2} \ln \relax (2)-50 x^{2}\right ) \ln \left (x^{4}\right ) {\mathrm e}^{\frac {\ln \left (\frac {\ln \left (x^{4}\right )}{3}\right )}{x}}+\left (4 x^{2} \ln \relax (2)^{2}+100 x^{2} \ln \relax (2)+625 x^{2}\right ) \ln \left (x^{4}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 40, normalized size = 1.54 \begin {gather*} -\frac {12 \cdot 3^{\left (\frac {1}{x}\right )}}{3^{\left (\frac {1}{x}\right )} {\left (2 \, \log \relax (2) + 25\right )} - e^{\left (\frac {2 \, \log \relax (2)}{x} + \frac {\log \left (\log \relax (x)\right )}{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.33, size = 63, normalized size = 2.42 \begin {gather*} -\frac {24\,\mathrm {atanh}\left (\frac {\ln \left (16\right )-\frac {2\,{\ln \left (x^4\right )}^{1/x}}{3^{1/x}}+50}{\sqrt {\ln \left (16\right )-2\,\ln \relax (4)}\,\sqrt {2\,\ln \relax (4)+\ln \left (16\right )+100}}\right )}{\sqrt {\ln \left (16\right )-2\,\ln \relax (4)}\,\sqrt {2\,\ln \relax (4)+\ln \left (16\right )+100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.38, size = 19, normalized size = 0.73 \begin {gather*} \frac {12}{e^{\frac {\log {\left (\frac {\log {\left (x^{4} \right )}}{3} \right )}}{x}} - 25 - 2 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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