Optimal. Leaf size=37 \[ \frac {4 e^{-e^5-i \pi +\frac {4}{x}+2 x}}{\left (2-\sqrt [4]{e}\right ) x} \]
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Rubi [B] Both result and optimal contain complex but leaf count is larger than twice the leaf
count of optimal. \(115\) vs. \(2(37)=74\).
time = 0.11, antiderivative size = 115, normalized size of antiderivative = 3.11, number of steps
used = 1, number of rules used = 1, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2326}
\begin {gather*} \frac {8 \left (2-x^2\right ) e^{\frac {2 x^2-e^5 x-x \left (\log \left (2-\sqrt [4]{e}\right )+i \pi \right )+4}{x}}}{x^3 \left (\frac {2 x^2-e^5 x-x \left (\log \left (2-\sqrt [4]{e}\right )+i \pi \right )+4}{x^2}+\frac {-4 x+i \pi +e^5+\log \left (2-\sqrt [4]{e}\right )}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {8 e^{\frac {4-e^5 x+2 x^2-x \left (i \pi +\log \left (2-\sqrt [4]{e}\right )\right )}{x}} \left (2-x^2\right )}{x^3 \left (\frac {e^5+i \pi -4 x+\log \left (2-\sqrt [4]{e}\right )}{x}+\frac {4-e^5 x+2 x^2-x \left (i \pi +\log \left (2-\sqrt [4]{e}\right )\right )}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 30, normalized size = 0.81 \begin {gather*} \frac {4 e^{-e^5+\frac {4}{x}+2 x}}{\left (-2+\sqrt [4]{e}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.22, size = 29, normalized size = 0.78
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{-\frac {x \,{\mathrm e}^{5}-2 x^{2}-4}{x}}}{x \left ({\mathrm e}^{\frac {1}{4}}-2\right )}\) | \(29\) |
gosper | \(\frac {4 \,{\mathrm e}^{-\frac {x \ln \left ({\mathrm e}^{\frac {1}{4}}-2\right )+x \,{\mathrm e}^{5}-2 x^{2}-4}{x}}}{x}\) | \(31\) |
norman | \(\frac {4 \,{\mathrm e}^{-\frac {x \ln \left ({\mathrm e}^{\frac {1}{4}}-2\right )+x \,{\mathrm e}^{5}-2 x^{2}-4}{x}}}{x}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 28, normalized size = 0.76 \begin {gather*} \frac {4 \, e^{\left (2 \, x + \frac {4}{x}\right )}}{x {\left (e^{\left (e^{5} + \frac {1}{4}\right )} - 2 \, e^{\left (e^{5}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 30, normalized size = 0.81 \begin {gather*} \frac {4 \, e^{\left (\frac {2 \, x^{2} - x e^{5} - x \log \left (e^{\frac {1}{4}} - 2\right ) + 4}{x}\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 [A]
time = 0.41, size = 29, normalized size = 0.78 \begin {gather*} \frac {4 \, e^{\left (\frac {2 \, x^{2} - x e^{5} + 4}{x}\right )}}{x e^{\frac {1}{4}} - 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.91, size = 26, normalized size = 0.70 \begin {gather*} \frac {4\,{\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{4/x}}{x\,\left ({\mathrm {e}}^{1/4}-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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