Optimal. Leaf size=19 \[ 5 e^{\log ^2\left (\frac {x^2 \log (5)}{\log \left (x^3\right )}\right )} \]
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Rubi [A]
time = 0.60, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 4, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6873, 12, 6874,
6838} \begin {gather*} 5 e^{\log ^2\left (\frac {x^2 \log (5)}{\log \left (x^3\right )}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 e^{\log ^2\left (\frac {x^2 \log (5)}{\log \left (x^3\right )}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 19, normalized size = 1.00 \begin {gather*} 5 e^{\log ^2\left (\frac {x^2 \log (5)}{\log \left (x^3\right )}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 2.23, size = 0, normalized size = 0.00 \[\int \frac {\left (20 \ln \left (x^{3}\right )-30\right ) \ln \left (\frac {x^{2} \ln \left (5\right )}{\ln \left (x^{3}\right )}\right ) {\mathrm e}^{\ln \left (\frac {x^{2} \ln \left (5\right )}{\ln \left (x^{3}\right )}\right )^{2}}}{x \ln \left (x^{3}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 68 vs.
\(2 (18) = 36\).
time = 0.64, size = 68, normalized size = 3.58 \begin {gather*} \frac {5 \, e^{\left (\log \left (3\right )^{2} - 4 \, \log \left (3\right ) \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + 4 \, \log \left (x\right ) \log \left (\log \left (5\right )\right ) + \log \left (\log \left (5\right )\right )^{2} + 2 \, \log \left (3\right ) \log \left (\log \left (x\right )\right ) - 4 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 2 \, \log \left (\log \left (5\right )\right ) \log \left (\log \left (x\right )\right ) + \log \left (\log \left (x\right )\right )^{2}\right )}}{3^{2 \, \log \left (\log \left (5\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 18, normalized size = 0.95 \begin {gather*} 5 \, e^{\left (\log \left (\frac {x^{2} \log \left (5\right )}{\log \left (x^{3}\right )}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 17, normalized size = 0.89 \begin {gather*} 5 e^{\log {\left (\frac {x^{2} \log {\left (5 \right )}}{\log {\left (x^{3} \right )}} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 18, normalized size = 0.95 \begin {gather*} 5 \, e^{\left (\log \left (\frac {x^{2} \log \left (5\right )}{\log \left (x^{3}\right )}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.26, size = 51, normalized size = 2.68 \begin {gather*} 5\,{\mathrm {e}}^{{\ln \left (x^2\right )}^2}\,{\mathrm {e}}^{{\ln \left (\ln \left (5\right )\right )}^2}\,{\mathrm {e}}^{{\ln \left (\frac {1}{\ln \left (x^3\right )}\right )}^2}\,{\left (\frac {1}{\ln \left (x^3\right )}\right )}^{2\,\ln \left (x^2\right )+2\,\ln \left (\ln \left (5\right )\right )}\,{\left (x^4\right )}^{\ln \left (\ln \left (5\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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