Optimal. Leaf size=18 \[ e^{e^{e^2+\frac {4}{x}-x} x} \]
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Rubi [F]
time = 0.56, 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 {e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}} \left (-4+x-x^2\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}}-\frac {4 e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}}}{x}-e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}} x\right ) \, dx\\ &=-\left (4 \int \frac {e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}}}{x} \, dx\right )+\int e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}} \, dx-\int e^{e^{\frac {4+e^2 x-x^2}{x}} x+\frac {4+e^2 x-x^2}{x}} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 18, normalized size = 1.00 \begin {gather*} e^{e^{e^2+\frac {4}{x}-x} x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 7.46, size = 20, normalized size = 1.11
method | result | size |
norman | \({\mathrm e}^{x \,{\mathrm e}^{\frac {{\mathrm e}^{2} x -x^{2}+4}{x}}}\) | \(20\) |
risch | \({\mathrm e}^{x \,{\mathrm e}^{\frac {{\mathrm e}^{2} x -x^{2}+4}{x}}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (x e^{\left (-x + \frac {4}{x} + e^{2}\right )}\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. 51 vs.
\(2 (15) = 30\).
time = 0.39, size = 51, normalized size = 2.83 \begin {gather*} e^{\left (\frac {x^{2} e^{\left (-\frac {x^{2} - x e^{2} - 4}{x}\right )} - x^{2} + x e^{2} + 4}{x} + \frac {x^{2} - x e^{2} - 4}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 15, normalized size = 0.83 \begin {gather*} e^{x e^{\frac {- x^{2} + x e^{2} + 4}{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 = 3.67, size = 16, normalized size = 0.89 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{4/x}\,{\mathrm {e}}^{{\mathrm {e}}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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