Optimal. Leaf size=25 \[ \frac {e^{e^{1+\frac {1}{2} (-4-x+18 \log (3))^2}}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(124\) vs. \(2(25)=50\).
time = 0.64, antiderivative size = 124, normalized size of antiderivative = 4.96, number of steps
used = 1, number of rules used = 1, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {2326}
\begin {gather*} \frac {\left (x^2+4 x-18 x \log (3)\right ) \exp \left (\frac {1}{2} \left (-x^2-8 x+36 (x+4) \log (3)-18 \left (1+18 \log ^2(3)\right )\right )+3^{\frac {1}{2} (-36 x-144)} e^{\frac {1}{2} \left (x^2+8 x+18 \left (1+18 \log ^2(3)\right )\right )}+\frac {1}{2} \left (x^2+8 x-36 (x+4) \log (3)+18 \left (1+18 \log ^2(3)\right )\right )\right )}{x^2 (x+2 (2-9 \log (3)))} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\exp \left (3^{\frac {1}{2} (-144-36 x)} e^{\frac {1}{2} \left (8 x+x^2+18 \left (1+18 \log ^2(3)\right )\right )}+\frac {1}{2} \left (-8 x-x^2+36 (4+x) \log (3)-18 \left (1+18 \log ^2(3)\right )\right )+\frac {1}{2} \left (8 x+x^2-36 (4+x) \log (3)+18 \left (1+18 \log ^2(3)\right )\right )\right ) \left (4 x+x^2-18 x \log (3)\right )}{x^2 (x+2 (2-9 \log (3)))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 34, normalized size = 1.36 \begin {gather*} \frac {e^{3^{-72-18 x} e^{9+4 x+\frac {x^2}{2}+162 \log ^2(3)}}}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.72, size = 31, normalized size = 1.24
method | result | size |
risch | \(\frac {{\mathrm e}^{3^{-72-18 x} {\mathrm e}^{162 \ln \left (3\right )^{2}+9+\frac {x^{2}}{2}+4 x}}}{x}\) | \(31\) |
norman | \(\frac {{\mathrm e}^{{\mathrm e}^{162 \ln \left (3\right )^{2}+\frac {\left (-36 x -144\right ) \ln \left (3\right )}{2}+\frac {x^{2}}{2}+4 x +9}}}{x}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.81, size = 29, normalized size = 1.16 \begin {gather*} \frac {e^{\left (\frac {1}{22528399544939174411840147874772641} \, e^{\left (\frac {1}{2} \, x^{2} - 18 \, x \log \left (3\right ) + 162 \, \log \left (3\right )^{2} + 4 \, x + 9\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 29, normalized size = 1.16 \begin {gather*} \frac {e^{\left (e^{\left (\frac {1}{2} \, x^{2} - 18 \, {\left (x + 4\right )} \log \left (3\right ) + 162 \, \log \left (3\right )^{2} + 4 \, x + 9\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 31, normalized size = 1.24 \begin {gather*} \frac {e^{e^{\frac {x^{2}}{2} + 4 x + \left (- 18 x - 72\right ) \log {\left (3 \right )} + 9 + 162 \log {\left (3 \right )}^{2}}}}{x} \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 = 5.82, size = 29, normalized size = 1.16 \begin {gather*} \frac {{\mathrm {e}}^{\frac {{\left (\frac {1}{387420489}\right )}^x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^9\,{\mathrm {e}}^{162\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{\frac {x^2}{2}}}{22528399544939174411840147874772641}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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