Optimal. Leaf size=26 \[ \frac {e^{1+\frac {81}{25 x^2}} (-1+x)^2}{x \log \left (x^2\right )} \]
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Rubi [F]
time = 1.98, 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 (\frac {81+25 x^2+25 x^2 \log \left (1-2 x+x^2\right )-25 x^2 \log \left (\log \left (x^2\right )\right )}{25 x^2}\right ) \left (50 x^2-50 x^3+\left (162-162 x+25 x^2+25 x^3\right ) \log \left (x^2\right )\right )}{\left (-25 x^4+25 x^5\right ) \log \left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {81+25 x^2+25 x^2 \log \left (1-2 x+x^2\right )-25 x^2 \log \left (\log \left (x^2\right )\right )}{25 x^2}\right ) \left (50 x^2-50 x^3+\left (162-162 x+25 x^2+25 x^3\right ) \log \left (x^2\right )\right )}{x^4 (-25+25 x) \log \left (x^2\right )} \, dx\\ &=\int \frac {e^{1+\frac {81}{25 x^2}} (1-x) \left (50 (-1+x) x^2-\left (162-162 x+25 x^2+25 x^3\right ) \log \left (x^2\right )\right )}{25 x^4 \log ^2\left (x^2\right )} \, dx\\ &=\frac {1}{25} \int \frac {e^{1+\frac {81}{25 x^2}} (1-x) \left (50 (-1+x) x^2-\left (162-162 x+25 x^2+25 x^3\right ) \log \left (x^2\right )\right )}{x^4 \log ^2\left (x^2\right )} \, dx\\ &=\frac {1}{25} \int \left (-\frac {50 e^{1+\frac {81}{25 x^2}} (-1+x)^2}{x^2 \log ^2\left (x^2\right )}+\frac {e^{1+\frac {81}{25 x^2}} \left (-162+324 x-187 x^2+25 x^4\right )}{x^4 \log \left (x^2\right )}\right ) \, dx\\ &=\frac {1}{25} \int \frac {e^{1+\frac {81}{25 x^2}} \left (-162+324 x-187 x^2+25 x^4\right )}{x^4 \log \left (x^2\right )} \, dx-2 \int \frac {e^{1+\frac {81}{25 x^2}} (-1+x)^2}{x^2 \log ^2\left (x^2\right )} \, dx\\ &=\frac {1}{25} \int \left (\frac {25 e^{1+\frac {81}{25 x^2}}}{\log \left (x^2\right )}-\frac {162 e^{1+\frac {81}{25 x^2}}}{x^4 \log \left (x^2\right )}+\frac {324 e^{1+\frac {81}{25 x^2}}}{x^3 \log \left (x^2\right )}-\frac {187 e^{1+\frac {81}{25 x^2}}}{x^2 \log \left (x^2\right )}\right ) \, dx-2 \int \left (\frac {e^{1+\frac {81}{25 x^2}}}{\log ^2\left (x^2\right )}+\frac {e^{1+\frac {81}{25 x^2}}}{x^2 \log ^2\left (x^2\right )}-\frac {2 e^{1+\frac {81}{25 x^2}}}{x \log ^2\left (x^2\right )}\right ) \, dx\\ &=-\left (2 \int \frac {e^{1+\frac {81}{25 x^2}}}{\log ^2\left (x^2\right )} \, dx\right )-2 \int \frac {e^{1+\frac {81}{25 x^2}}}{x^2 \log ^2\left (x^2\right )} \, dx+4 \int \frac {e^{1+\frac {81}{25 x^2}}}{x \log ^2\left (x^2\right )} \, dx-\frac {162}{25} \int \frac {e^{1+\frac {81}{25 x^2}}}{x^4 \log \left (x^2\right )} \, dx-\frac {187}{25} \int \frac {e^{1+\frac {81}{25 x^2}}}{x^2 \log \left (x^2\right )} \, dx+\frac {324}{25} \int \frac {e^{1+\frac {81}{25 x^2}}}{x^3 \log \left (x^2\right )} \, dx+\int \frac {e^{1+\frac {81}{25 x^2}}}{\log \left (x^2\right )} \, dx\\ &=-\left (2 \int \frac {e^{1+\frac {81}{25 x^2}}}{\log ^2\left (x^2\right )} \, dx\right )-2 \int \frac {e^{1+\frac {81}{25 x^2}}}{x^2 \log ^2\left (x^2\right )} \, dx+2 \text {Subst}\left (\int \frac {e^{1+\frac {81}{25 x}}}{x \log ^2(x)} \, dx,x,x^2\right )-\frac {162}{25} \int \frac {e^{1+\frac {81}{25 x^2}}}{x^4 \log \left (x^2\right )} \, dx+\frac {162}{25} \text {Subst}\left (\int \frac {e^{1+\frac {81}{25 x}}}{x^2 \log (x)} \, dx,x,x^2\right )-\frac {187}{25} \int \frac {e^{1+\frac {81}{25 x^2}}}{x^2 \log \left (x^2\right )} \, dx+\int \frac {e^{1+\frac {81}{25 x^2}}}{\log \left (x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} \frac {e^{1+\frac {81}{25 x^2}} (-1+x)^2}{x \log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.19, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (25 x^{3}+25 x^{2}-162 x +162\right ) \ln \left (x^{2}\right )-50 x^{3}+50 x^{2}\right ) {\mathrm e}^{\frac {-25 x^{2} \ln \left (\ln \left (x^{2}\right )\right )+25 x^{2} \ln \left (x^{2}-2 x +1\right )+25 x^{2}+81}{25 x^{2}}}}{\left (25 x^{5}-25 x^{4}\right ) \ln \left (x^{2}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 41, normalized size = 1.58 \begin {gather*} \frac {e^{\left (\frac {25 \, x^{2} \log \left (x^{2} - 2 \, x + 1\right ) - 25 \, x^{2} \log \left (\log \left (x^{2}\right )\right ) + 25 \, x^{2} + 81}{25 \, x^{2}}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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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 = 0.83, size = 23, normalized size = 0.88 \begin {gather*} \frac {{\mathrm {e}}^{\frac {81}{25\,x^2}+1}\,{\left (x-1\right )}^2}{x\,\ln \left (x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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