Optimal. Leaf size=23 \[ e^{-5 e^2 x+\frac {3 x}{\log (x)}} \log \left (16 x^4\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(23)=46\).
time = 0.20, antiderivative size = 93, normalized size of antiderivative = 4.04, number of steps
used = 1, number of rules used = 1, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2326}
\begin {gather*} -\frac {e^{\frac {3 x}{\log (x)}-5 e^2 x} \left (3 x+5 e^2 x \log ^2(x)-3 x \log (x)\right ) \log \left (16 x^4\right )}{x \log ^2(x) \left (\frac {-5 e^2 \log (x)-5 e^2+3}{\log (x)}-\frac {3 x-5 e^2 x \log (x)}{x \log ^2(x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{-5 e^2 x+\frac {3 x}{\log (x)}} \left (3 x-3 x \log (x)+5 e^2 x \log ^2(x)\right ) \log \left (16 x^4\right )}{x \log ^2(x) \left (\frac {3-5 e^2-5 e^2 \log (x)}{\log (x)}-\frac {3 x-5 e^2 x \log (x)}{x \log ^2(x)}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 23, normalized size = 1.00 \begin {gather*} e^{-5 e^2 x+\frac {3 x}{\log (x)}} \log \left (16 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 6.97, size = 46, normalized size = 2.00
method | result | size |
default | \(\frac {\left (\left (\ln \left (16 x^{4}\right )-4 \ln \left (x \right )\right ) \ln \left (x \right )+4 \ln \left (x \right )^{2}\right ) {\mathrm e}^{-\frac {5 x \,{\mathrm e}^{2} \ln \left (x \right )-3 x}{\ln \left (x \right )}}}{\ln \left (x \right )}\) | \(46\) |
risch | \(\left (4 \ln \left (2\right )+4 \ln \left (x \right )-\frac {i \pi \mathrm {csgn}\left (i x^{3}\right )^{3}}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right )^{2}}{2}+\frac {i \pi \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x \right )}{2}-\frac {i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}-\frac {i \pi \mathrm {csgn}\left (i x^{4}\right )^{3}}{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x^{4}\right ) \mathrm {csgn}\left (i x \right )}{2}+\frac {i \pi \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}+\frac {i \pi \mathrm {csgn}\left (i x^{4}\right )^{2} \mathrm {csgn}\left (i x \right )}{2}\right ) {\mathrm e}^{-\frac {x \left (5 \,{\mathrm e}^{2} \ln \left (x \right )-3\right )}{\ln \left (x \right )}}\) | \(224\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 21, normalized size = 0.91 \begin {gather*} 4 \, {\left (\log \left (2\right ) + \log \left (x\right )\right )} e^{\left (-5 \, x e^{2} + \frac {3 \, x}{\log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 25, normalized size = 1.09 \begin {gather*} 4 \, {\left (\log \left (2\right ) + \log \left (x\right )\right )} e^{\left (-\frac {5 \, x e^{2} \log \left (x\right ) - 3 \, x}{\log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.29, size = 27, normalized size = 1.17 \begin {gather*} \left (4 \log {\left (x \right )} + 4 \log {\left (2 \right )}\right ) e^{- \frac {5 x e^{2} \log {\left (x \right )} - 3 x}{\log {\left (x \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 45 vs.
\(2 (21) = 42\).
time = 0.44, size = 45, normalized size = 1.96 \begin {gather*} 4 \, e^{\left (-\frac {5 \, x e^{2} \log \left (x\right ) - 3 \, x}{\log \left (x\right )}\right )} \log \left (2\right ) + 4 \, e^{\left (-\frac {5 \, x e^{2} \log \left (x\right ) - 3 \, x}{\log \left (x\right )}\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.53, size = 21, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{\frac {3\,x}{\ln \left (x\right )}-5\,x\,{\mathrm {e}}^2}\,\ln \left (16\,x^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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