Optimal. Leaf size=23 \[ \frac {e^{e^{x^2}}}{\left (-\frac {5 x}{-1+e^3}+\log (x)\right )^2} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(144\) vs. \(2(23)=46\).
time = 1.00, antiderivative size = 144, normalized size of antiderivative = 6.26, number of steps
used = 1, number of rules used = 1, integrand size = 180, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {2326}
\begin {gather*} \frac {e^{e^{x^2}-x^2} \left (e^{x^2} \left (-e^9 x^2+3 e^6 x^2-3 e^3 x^2+x^2\right ) \log (x)+5 e^{x^2} \left (e^6 x^3-2 e^3 x^3+x^3\right )\right )}{x \left (125 x^4+75 \left (x^3-e^3 x^3\right ) \log (x)+15 \left (e^6 x^2-2 e^3 x^2+x^2\right ) \log ^2(x)+\left (1-e^3\right )^3 x \log ^3(x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{e^{x^2}-x^2} \left (5 e^{x^2} \left (x^3-2 e^3 x^3+e^6 x^3\right )+e^{x^2} \left (x^2-3 e^3 x^2+3 e^6 x^2-e^9 x^2\right ) \log (x)\right )}{x \left (125 x^4+75 \left (x^3-e^3 x^3\right ) \log (x)+15 \left (x^2-2 e^3 x^2+e^6 x^2\right ) \log ^2(x)+\left (1-e^3\right )^3 x \log ^3(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.38, size = 30, normalized size = 1.30 \begin {gather*} \frac {e^{e^{x^2}} \left (-1+e^3\right )^2}{\left (5 x+\log (x)-e^3 \log (x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 30, normalized size = 1.30
method | result | size |
risch | \(\frac {\left ({\mathrm e}^{6}-2 \,{\mathrm e}^{3}+1\right ) {\mathrm e}^{{\mathrm e}^{x^{2}}}}{\left (\ln \left (x \right ) {\mathrm e}^{3}-\ln \left (x \right )-5 x \right )^{2}}\) | \(30\) |
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. 46 vs.
\(2 (22) = 44\).
time = 0.32, size = 46, normalized size = 2.00 \begin {gather*} -\frac {{\left (e^{6} - 2 \, e^{3} + 1\right )} e^{\left (e^{\left (x^{2}\right )}\right )}}{10 \, x {\left (e^{3} - 1\right )} \log \left (x\right ) - {\left (e^{6} - 2 \, e^{3} + 1\right )} \log \left (x\right )^{2} - 25 \, x^{2}} \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. 47 vs.
\(2 (22) = 44\).
time = 0.40, size = 47, normalized size = 2.04 \begin {gather*} \frac {{\left (e^{6} - 2 \, e^{3} + 1\right )} e^{\left (e^{\left (x^{2}\right )}\right )}}{{\left (e^{6} - 2 \, e^{3} + 1\right )} \log \left (x\right )^{2} + 25 \, x^{2} - 10 \, {\left (x e^{3} - x\right )} \log \left (x\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. 61 vs.
\(2 (19) = 38\).
time = 0.25, size = 61, normalized size = 2.65 \begin {gather*} \frac {\left (- 2 e^{3} + 1 + e^{6}\right ) e^{e^{x^{2}}}}{25 x^{2} - 10 x e^{3} \log {\left (x \right )} + 10 x \log {\left (x \right )} - 2 e^{3} \log {\left (x \right )}^{2} + \log {\left (x \right )}^{2} + e^{6} \log {\left (x \right )}^{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 = 9.79, size = 26, normalized size = 1.13 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\,{\left ({\mathrm {e}}^3-1\right )}^2}{{\left (5\,x-\ln \left (x\right )\,\left ({\mathrm {e}}^3-1\right )\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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