Optimal. Leaf size=26 \[ \frac {32 e^{-2 x} \log ^2(x)}{3 x^2 \log ^2\left (\frac {x^2}{4}\right )} \]
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Rubi [F]
time = 3.78, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{-2 x} \log (x) \left (-128 \log (x)+(64+(-64-64 x) \log (x)) \log \left (\frac {x^2}{4}\right )\right )}{3 x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {e^{-2 x} \log (x) \left (-128 \log (x)+(64+(-64-64 x) \log (x)) \log \left (\frac {x^2}{4}\right )\right )}{x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx\\ &=\frac {1}{3} \int \left (-\frac {128 e^{-2 x} \log ^2(x)}{x^3 \log ^3\left (\frac {x^2}{4}\right )}-\frac {64 e^{-2 x} \log (x) (-1+\log (x)+x \log (x))}{x^3 \log ^2\left (\frac {x^2}{4}\right )}\right ) \, dx\\ &=-\left (\frac {64}{3} \int \frac {e^{-2 x} \log (x) (-1+\log (x)+x \log (x))}{x^3 \log ^2\left (\frac {x^2}{4}\right )} \, dx\right )-\frac {128}{3} \int \frac {e^{-2 x} \log ^2(x)}{x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx\\ &=-\left (\frac {64}{3} \int \left (-\frac {e^{-2 x} \log (x)}{x^3 \log ^2\left (\frac {x^2}{4}\right )}+\frac {e^{-2 x} \log ^2(x)}{x^3 \log ^2\left (\frac {x^2}{4}\right )}+\frac {e^{-2 x} \log ^2(x)}{x^2 \log ^2\left (\frac {x^2}{4}\right )}\right ) \, dx\right )-\frac {128}{3} \int \frac {e^{-2 x} \log ^2(x)}{x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx\\ &=\frac {64}{3} \int \frac {e^{-2 x} \log (x)}{x^3 \log ^2\left (\frac {x^2}{4}\right )} \, dx-\frac {64}{3} \int \frac {e^{-2 x} \log ^2(x)}{x^3 \log ^2\left (\frac {x^2}{4}\right )} \, dx-\frac {64}{3} \int \frac {e^{-2 x} \log ^2(x)}{x^2 \log ^2\left (\frac {x^2}{4}\right )} \, dx-\frac {128}{3} \int \frac {e^{-2 x} \log ^2(x)}{x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] Contains unresolved integral.
time = 1.15, size = 51, normalized size = 1.96 \begin {gather*} \frac {1}{3} \int \frac {e^{-2 x} \log (x) \left (-128 \log (x)+(64+(-64-64 x) \log (x)) \log \left (\frac {x^2}{4}\right )\right )}{x^3 \log ^3\left (\frac {x^2}{4}\right )} \, dx \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.41, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (-64 x -64\right ) \ln \left (x \right )+64\right ) \ln \left (\frac {x^{2}}{4}\right )-128 \ln \left (x \right )\right ) \ln \left (x \right ) {\mathrm e}^{-2 x}}{3 \ln \left (\frac {x^{2}}{4}\right )^{3} x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 38, normalized size = 1.46 \begin {gather*} \frac {8 \, e^{\left (-2 \, x\right )} \log \left (x\right )^{2}}{3 \, {\left (x^{2} \log \left (2\right )^{2} - 2 \, x^{2} \log \left (2\right ) \log \left (x\right ) + x^{2} \log \left (x\right )^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 26, normalized size = 1.00 \begin {gather*} \frac {32}{3} \, e^{\left (-2 \, x + 2 \, \log \left (-\frac {\log \left (x\right )}{2 \, {\left (x \log \left (2\right ) - x \log \left (x\right )\right )}}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 42, normalized size = 1.62 \begin {gather*} \frac {8 e^{- 2 x} \log {\left (x \right )}^{2}}{3 x^{2} \log {\left (x \right )}^{2} - 6 x^{2} \log {\left (2 \right )} \log {\left (x \right )} + 3 x^{2} \log {\left (2 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 24, normalized size = 0.92 \begin {gather*} \frac {32}{3} \, e^{\left (-2 \, x + 2 \, \log \left (\frac {\log \left (x\right )}{x \log \left (\frac {1}{4} \, x^{2}\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{2\,\ln \left (\frac {\ln \left (x\right )}{x\,\ln \left (\frac {x^2}{4}\right )}\right )-2\,x}\,\left (128\,\ln \left (x\right )+\ln \left (\frac {x^2}{4}\right )\,\left (\ln \left (x\right )\,\left (64\,x+64\right )-64\right )\right )}{3\,x\,\ln \left (\frac {x^2}{4}\right )\,\ln \left (x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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