Optimal. Leaf size=30 \[ \frac {1}{2} e^{-\frac {20 e^{e^x}}{x}} \left (\frac {4}{x}+x\right ) \left (5-x^2\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(74\) vs. \(2(30)=60\).
time = 0.15, antiderivative size = 74, normalized size of antiderivative = 2.47, number of steps
used = 2, number of rules used = 2, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {12, 2326}
\begin {gather*} \frac {e^{e^x-\frac {20 e^{e^x}}{x}} \left (-x^4+x^2-e^x \left (-x^5+x^3+20 x\right )+20\right )}{2 \left (\frac {e^{e^x}}{x^2}-\frac {e^{x+e^x}}{x}\right ) x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {e^{-\frac {20 e^{e^x}}{x}} \left (-20 x+x^3-3 x^5+e^{e^x} \left (400+20 x^2-20 x^4+e^x \left (-400 x-20 x^3+20 x^5\right )\right )\right )}{x^3} \, dx\\ &=\frac {e^{e^x-\frac {20 e^{e^x}}{x}} \left (20+x^2-x^4-e^x \left (20 x+x^3-x^5\right )\right )}{2 \left (\frac {e^{e^x}}{x^2}-\frac {e^{e^x+x}}{x}\right ) x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.38, size = 29, normalized size = 0.97 \begin {gather*} \frac {e^{-\frac {20 e^{e^x}}{x}} \left (20+x^2-x^4\right )}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 25, normalized size = 0.83
method | result | size |
risch | \(-\frac {\left (x^{4}-x^{2}-20\right ) {\mathrm e}^{-\frac {20 \,{\mathrm e}^{{\mathrm e}^{x}}}{x}}}{2 x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.58, size = 24, normalized size = 0.80 \begin {gather*} -\frac {{\left (x^{4} - x^{2} - 20\right )} e^{\left (-\frac {20 \, e^{\left (e^{x}\right )}}{x}\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 24, normalized size = 0.80 \begin {gather*} -\frac {{\left (x^{4} - x^{2} - 20\right )} e^{\left (-\frac {20 \, e^{\left (e^{x}\right )}}{x}\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 20, normalized size = 0.67 \begin {gather*} \frac {\left (- x^{4} + x^{2} + 20\right ) e^{- \frac {20 e^{e^{x}}}{x}}}{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 = 0.47, size = 24, normalized size = 0.80 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {20\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x}}\,\left (-x^4+x^2+20\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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