Optimal. Leaf size=20 \[ e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}}+e^{x^2} \]
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Rubi [A]
time = 0.41, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 5, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.104, Rules used = {14, 2240, 6847,
2320, 2225} \begin {gather*} e^{x^2}+e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rule 2240
Rule 2320
Rule 6847
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 e^{x^2} x-\frac {2 e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}+\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}} \log ^2\left (\frac {174}{7}\right )}{x^3}\right ) \, dx\\ &=2 \int e^{x^2} x \, dx-\left (2 \log ^2\left (\frac {174}{7}\right )\right ) \int \frac {e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}+\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}}{x^3} \, dx\\ &=e^{x^2}+\log ^2\left (\frac {174}{7}\right ) \text {Subst}\left (\int e^{e^{x \log ^2\left (\frac {174}{7}\right )}+x \log ^2\left (\frac {174}{7}\right )} \, dx,x,\frac {1}{x^2}\right )\\ &=e^{x^2}+\text {Subst}\left (\int e^x \, dx,x,e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}\right )\\ &=e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}}+e^{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.20, size = 20, normalized size = 1.00 \begin {gather*} e^{e^{\frac {\log ^2\left (\frac {174}{7}\right )}{x^2}}}+e^{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.71, size = 16, normalized size = 0.80
method | result | size |
default | \({\mathrm e}^{x^{2}}+{\mathrm e}^{{\mathrm e}^{\frac {\ln \left (\frac {174}{7}\right )^{2}}{x^{2}}}}\) | \(16\) |
risch | \({\mathrm e}^{x^{2}}+{\mathrm e}^{{\mathrm e}^{\frac {\left (\ln \left (2\right )+\ln \left (3\right )+\ln \left (29\right )-\ln \left (7\right )\right )^{2}}{x^{2}}}}\) | \(25\) |
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. 148 vs.
\(2 (15) = 30\).
time = 0.53, size = 148, normalized size = 7.40 \begin {gather*} \frac {e^{\left (e^{\left (\frac {\log \left (29\right )^{2}}{x^{2}} - \frac {2 \, \log \left (29\right ) \log \left (7\right )}{x^{2}} + \frac {\log \left (7\right )^{2}}{x^{2}} + \frac {2 \, \log \left (29\right ) \log \left (3\right )}{x^{2}} - \frac {2 \, \log \left (7\right ) \log \left (3\right )}{x^{2}} + \frac {\log \left (3\right )^{2}}{x^{2}} + \frac {2 \, \log \left (29\right ) \log \left (2\right )}{x^{2}} - \frac {2 \, \log \left (7\right ) \log \left (2\right )}{x^{2}} + \frac {2 \, \log \left (3\right ) \log \left (2\right )}{x^{2}} + \frac {\log \left (2\right )^{2}}{x^{2}}\right )}\right )} \log \left (\frac {174}{7}\right )^{2}}{\log \left (29\right )^{2} - 2 \, \log \left (29\right ) \log \left (7\right ) + \log \left (7\right )^{2} + 2 \, {\left (\log \left (29\right ) - \log \left (7\right )\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 2 \, {\left (\log \left (29\right ) - \log \left (7\right ) + \log \left (3\right )\right )} \log \left (2\right ) + \log \left (2\right )^{2}} + e^{\left (x^{2}\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. 48 vs.
\(2 (15) = 30\).
time = 0.42, size = 48, normalized size = 2.40 \begin {gather*} {\left (e^{\left (x^{2} + \frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} + e^{\left (\frac {x^{2} e^{\left (\frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} + \log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )}\right )} e^{\left (-\frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 17, normalized size = 0.85 \begin {gather*} e^{x^{2}} + e^{e^{\frac {\log {\left (\frac {174}{7} \right )}^{2}}{x^{2}}}} \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. 48 vs.
\(2 (15) = 30\).
time = 0.49, size = 48, normalized size = 2.40 \begin {gather*} {\left (e^{\left (x^{2} + \frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} + e^{\left (\frac {x^{2} e^{\left (\frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} + \log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )}\right )} e^{\left (-\frac {\log \left (\frac {174}{7}\right )^{2}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.84, size = 36, normalized size = 1.80 \begin {gather*} {\mathrm {e}}^{x^2}+{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {{\ln \left (7\right )}^2}{x^2}}\,{\mathrm {e}}^{\frac {{\ln \left (174\right )}^2}{x^2}}}{7^{\frac {2\,\ln \left (174\right )}{x^2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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