Optimal. Leaf size=27 \[ \frac {1}{2} e^{\left (3+\frac {4 \log ^2(2)}{\log ^2(x)}\right )^2} (5 x+\log (\log (5))) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(141\) vs. \(2(27)=54\).
time = 0.54, antiderivative size = 141, normalized size of antiderivative = 5.22, number of steps
used = 2, number of rules used = 2, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {12, 2326}
\begin {gather*} -\frac {2 \left (20 x \log ^4(2)+15 x \log ^2(2) \log ^2(x)+\log (\log (5)) \left (3 \log ^2(2) \log ^2(x)+4 \log ^4(2)\right )\right ) \exp \left (\frac {9 \log ^4(x)+24 \log ^2(2) \log ^2(x)+16 \log ^4(2)}{\log ^4(x)}\right )}{x \log ^5(x) \left (\frac {3 \left (\frac {3 \log ^3(x)}{x}+\frac {4 \log ^2(2) \log (x)}{x}\right )}{\log ^4(x)}-\frac {9 \log ^4(x)+24 \log ^2(2) \log ^2(x)+16 \log ^4(2)}{x \log ^5(x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {\exp \left (\frac {16 \log ^4(2)+24 \log ^2(2) \log ^2(x)+9 \log ^4(x)}{\log ^4(x)}\right ) \left (-320 x \log ^4(2)-240 x \log ^2(2) \log ^2(x)+5 x \log ^5(x)+\left (-64 \log ^4(2)-48 \log ^2(2) \log ^2(x)\right ) \log (\log (5))\right )}{x \log ^5(x)} \, dx\\ &=-\frac {2 \exp \left (\frac {16 \log ^4(2)+24 \log ^2(2) \log ^2(x)+9 \log ^4(x)}{\log ^4(x)}\right ) \left (20 x \log ^4(2)+15 x \log ^2(2) \log ^2(x)+\left (4 \log ^4(2)+3 \log ^2(2) \log ^2(x)\right ) \log (\log (5))\right )}{x \log ^5(x) \left (\frac {3 \left (\frac {4 \log ^2(2) \log (x)}{x}+\frac {3 \log ^3(x)}{x}\right )}{\log ^4(x)}-\frac {16 \log ^4(2)+24 \log ^2(2) \log ^2(x)+9 \log ^4(x)}{x \log ^5(x)}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 33, normalized size = 1.22 \begin {gather*} \frac {1}{2} e^{\frac {\left (4 \log ^2(2)+3 \log ^2(x)\right )^2}{\log ^4(x)}} (5 x+\log (\log (5))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 31, normalized size = 1.15
method | result | size |
risch | \(\frac {\left (5 x +\ln \left (\ln \left (5\right )\right )\right ) {\mathrm e}^{\frac {\left (3 \ln \left (x \right )^{2}+4 \ln \left (2\right )^{2}\right )^{2}}{\ln \left (x \right )^{4}}}}{2}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 38, normalized size = 1.41 \begin {gather*} \frac {1}{2} \, {\left (5 \, x + \log \left (\log \left (5\right )\right )\right )} e^{\left (\frac {16 \, \log \left (2\right )^{4} + 24 \, \log \left (2\right )^{2} \log \left (x\right )^{2} + 9 \, \log \left (x\right )^{4}}{\log \left (x\right )^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.37, size = 41, normalized size = 1.52 \begin {gather*} \frac {\left (5 x + \log {\left (\log {\left (5 \right )} \right )}\right ) e^{\frac {9 \log {\left (x \right )}^{4} + 24 \log {\left (2 \right )}^{2} \log {\left (x \right )}^{2} + 16 \log {\left (2 \right )}^{4}}{\log {\left (x \right )}^{4}}}}{2} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.70, size = 57, normalized size = 2.11 \begin {gather*} \frac {{\mathrm {e}}^9\,{\mathrm {e}}^{\frac {16\,{\ln \left (2\right )}^4}{{\ln \left (x\right )}^4}}\,{\mathrm {e}}^{\frac {24\,{\ln \left (2\right )}^2}{{\ln \left (x\right )}^2}}\,\ln \left (\ln \left (5\right )\right )}{2}+\frac {5\,x\,{\mathrm {e}}^9\,{\mathrm {e}}^{\frac {16\,{\ln \left (2\right )}^4}{{\ln \left (x\right )}^4}}\,{\mathrm {e}}^{\frac {24\,{\ln \left (2\right )}^2}{{\ln \left (x\right )}^2}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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