Optimal. Leaf size=19 \[ e^{3+\log ^2(x)} \log (5) \log \left (-\frac {5}{2 x^2}\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {2288} \begin {gather*} \log (5) e^{\log ^2(x)+3} \log \left (-\frac {5}{2 x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{3+\log ^2(x)} \log (5) \log \left (-\frac {5}{2 x^2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} e^{3+\log ^2(x)} \log (5) \log \left (-\frac {5}{2 x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [C] time = 0.64, size = 57, normalized size = 3.00 \begin {gather*} e^{\left (-\frac {1}{4} \, \pi ^{2} + \frac {1}{2} i \, \pi \log \left (\frac {5}{2}\right ) + \frac {1}{4} \, \log \left (\frac {5}{2}\right )^{2} - \frac {1}{2} i \, \pi \log \left (-\frac {5}{2 \, x^{2}}\right ) - \frac {1}{2} \, \log \left (\frac {5}{2}\right ) \log \left (-\frac {5}{2 \, x^{2}}\right ) + \frac {1}{4} \, \log \left (-\frac {5}{2 \, x^{2}}\right )^{2} + 3\right )} \log \relax (5) \log \left (-\frac {5}{2 \, x^{2}}\right ) \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 {2 \, {\left (\log \relax (5) \log \relax (x) \log \left (-\frac {5}{2 \, x^{2}}\right ) - \log \relax (5)\right )} e^{\left (\log \relax (x)^{2} + 3\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 36, normalized size = 1.89
method | result | size |
default | \({\mathrm e}^{3} \ln \relax (5) \left (\ln \left (-\frac {5}{2 x^{2}}\right )+2 \ln \relax (x )\right ) {\mathrm e}^{\ln \relax (x )^{2}}-2 \,{\mathrm e}^{3} \ln \relax (5) {\mathrm e}^{\ln \relax (x )^{2}} \ln \relax (x )\) | \(36\) |
risch | \(\left (\frac {i \ln \relax (5) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-i \ln \relax (5) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\frac {i \ln \relax (5) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}-i \ln \relax (5) \pi \mathrm {csgn}\left (\frac {i}{x^{2}}\right )^{2}+i \ln \relax (5) \pi \mathrm {csgn}\left (\frac {i}{x^{2}}\right )^{3}+i \ln \relax (5) \pi +\ln \relax (5)^{2}-\ln \relax (2) \ln \relax (5)-2 \ln \relax (5) \ln \relax (x )\right ) {\mathrm e}^{\ln \relax (x )^{2}+3}\) | \(117\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 16, normalized size = 0.84 \begin {gather*} e^{\left (\log \relax (x)^{2} + 3\right )} \log \relax (5) \log \left (-\frac {5}{2 \, x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.47, size = 21, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{{\ln \relax (x)}^2+3}\,\ln \relax (5)\,\left (\ln \left (\frac {5}{2\,x^2}\right )+\pi \,1{}\mathrm {i}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 0.52, size = 36, normalized size = 1.89 \begin {gather*} - \left (2 \log {\relax (5 )} \log {\relax (x )} - \log {\relax (5 )}^{2} + \log {\relax (2 )} \log {\relax (5 )} - i \pi \log {\relax (5 )}\right ) e^{\log {\relax (x )}^{2} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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