Optimal. Leaf size=27 \[ 5 e^{-\left (3-\log \left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )\right )^2} \]
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Rubi [B] time = 0.18, antiderivative size = 68, normalized size of antiderivative = 2.52, number of steps used = 2, number of rules used = 2, integrand size = 81, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {12, 2288} \begin {gather*} \frac {5 \left (1-8 x^2\right ) e^{-\log ^2\left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )-9} \left (4 x^2-\log (x)\right )^7}{16777216 \left (\frac {1}{x}-8 x\right ) \left (4 x^3-x \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{-9-\log ^2\left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )} \left (4 x^2-\log (x)\right )^6 \left (30-240 x^2+\left (-10+80 x^2\right ) \log \left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )\right )}{-4 x^3+x \log (x)} \, dx}{16777216}\\ &=\frac {5 e^{-9-\log ^2\left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )} \left (1-8 x^2\right ) \left (4 x^2-\log (x)\right )^7}{16777216 \left (\frac {1}{x}-8 x\right ) \left (4 x^3-x \log (x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 37, normalized size = 1.37 \begin {gather*} \frac {5 e^{-9-\log ^2\left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )} \left (-4 x^2+\log (x)\right )^6}{16777216} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 33, normalized size = 1.22 \begin {gather*} 5 \, e^{\left (-\log \left (\frac {1}{4} \, x^{2} - \frac {1}{16} \, \log \relax (x)\right )^{2} + 6 \, \log \left (\frac {1}{4} \, x^{2} - \frac {1}{16} \, \log \relax (x)\right ) - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.62, size = 33, normalized size = 1.22 \begin {gather*} 5 \, e^{\left (-\log \left (\frac {1}{4} \, x^{2} - \frac {1}{16} \, \log \relax (x)\right )^{2} + 6 \, \log \left (\frac {1}{4} \, x^{2} - \frac {1}{16} \, \log \relax (x)\right ) - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 33, normalized size = 1.22
method | result | size |
risch | \(5 \left (\frac {x^{2}}{4}-\frac {\ln \relax (x )}{16}\right )^{6} {\mathrm e}^{-\ln \left (\frac {x^{2}}{4}-\frac {\ln \relax (x )}{16}\right )^{2}-9}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.68, size = 94, normalized size = 3.48 \begin {gather*} \frac {5}{16777216} \, {\left (4096 \, x^{12} - 6144 \, x^{10} \log \relax (x) + 3840 \, x^{8} \log \relax (x)^{2} - 1280 \, x^{6} \log \relax (x)^{3} + 240 \, x^{4} \log \relax (x)^{4} - 24 \, x^{2} \log \relax (x)^{5} + \log \relax (x)^{6}\right )} e^{\left (-16 \, \log \relax (2)^{2} + 8 \, \log \relax (2) \log \left (4 \, x^{2} - \log \relax (x)\right ) - \log \left (4 \, x^{2} - \log \relax (x)\right )^{2} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.50, size = 181, normalized size = 6.70 \begin {gather*} \frac {5\,x^{12}\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}}{4096}+\frac {5\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,{\ln \relax (x)}^6}{16777216}-\frac {15\,x^2\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,{\ln \relax (x)}^5}{2097152}+\frac {75\,x^4\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,{\ln \relax (x)}^4}{1048576}-\frac {25\,x^6\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,{\ln \relax (x)}^3}{65536}+\frac {75\,x^8\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,{\ln \relax (x)}^2}{65536}-\frac {15\,x^{10}\,{\mathrm {e}}^{-{\ln \left (\frac {x^2}{4}-\frac {\ln \relax (x)}{16}\right )}^2-9}\,\ln \relax (x)}{8192} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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