Optimal. Leaf size=28 \[ e^{e^{\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}}} \]
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Rubi [F]
time = 109.53, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \frac {\exp \left (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \frac {\exp \left (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+2 x^2+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) (5+\log (x)) \left (37-80 x^2+\log (x)+4 x^2 \log (x)-2 \log ^2(x)+4 x^2 \log ^2(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) (5+\log (x)) \left (37-80 x^2+\left (1+4 x^2\right ) \log (x)+\left (-2+4 x^2\right ) \log ^2(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \left (-\frac {5 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-37+80 x^2\right )}{x^3}-\frac {6 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-7+10 x^2\right ) \log (x)}{x^3}+\frac {3 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-3+8 x^2\right ) \log ^2(x)}{x^3}+\frac {2 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-1+2 x^2\right ) \log ^3(x)}{x^3}\right ) \, dx\\ &=\frac {2}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-1+2 x^2\right ) \log ^3(x)}{x^3} \, dx+\frac {3}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-3+8 x^2\right ) \log ^2(x)}{x^3} \, dx-\frac {1}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-37+80 x^2\right )}{x^3} \, dx-\frac {6}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-7+10 x^2\right ) \log (x)}{x^3} \, dx\\ &=\frac {2}{625} \int \left (-\frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x^3}+\frac {2 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x}\right ) \, dx+\frac {3}{625} \int \left (-\frac {3 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x^3}+\frac {8 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x}\right ) \, dx-\frac {1}{125} \int \left (-\frac {37 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x^3}+\frac {80 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x}\right ) \, dx-\frac {6}{625} \int \left (-\frac {7 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x^3}+\frac {10 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x}\right ) \, dx\\ &=-\left (\frac {2}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x^3} \, dx\right )+\frac {4}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x} \, dx-\frac {9}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x^3} \, dx+\frac {24}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x} \, dx+\frac {42}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x^3} \, dx-\frac {12}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x} \, dx+\frac {37}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x^3} \, dx-\frac {16}{25} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.63, size = 47, normalized size = 1.68 \begin {gather*} e^{e^{\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}} x^{-\frac {3 e^{2 x^2}}{125 x^2}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 24, normalized size = 0.86
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x^{2}} \left (\ln \left (x \right )-4\right ) \left (5+\ln \left (x \right )\right )^{2}}{625 x^{2}}}}\) | \(24\) |
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. 57 vs.
\(2 (23) = 46\).
time = 1.52, size = 57, normalized size = 2.04 \begin {gather*} e^{\left (e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3}}{625 \, x^{2}} + \frac {6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2}}{625 \, x^{2}} - \frac {3 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )}{125 \, x^{2}} - \frac {4 \, e^{\left (2 \, x^{2}\right )}}{25 \, x^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 149 vs.
\(2 (23) = 46\).
time = 0.44, size = 149, normalized size = 5.32 \begin {gather*} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 625 \, x^{2} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}} - \frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (26) = 52\).
time = 12.86, size = 58, normalized size = 2.07 \begin {gather*} e^{e^{\frac {\frac {e^{2 x^{2}} \log {\left (x \right )}^{3}}{625} + \frac {6 e^{2 x^{2}} \log {\left (x \right )}^{2}}{625} - \frac {3 e^{2 x^{2}} \log {\left (x \right )}}{125} - \frac {4 e^{2 x^{2}}}{25}}{x^{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 = 4.75, size = 60, normalized size = 2.14 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^{2\,x^2}\,\ln \left (x\right )}{125\,x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^2}}{25\,x^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^3}{625\,x^2}}\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^2}{625\,x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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