Optimal. Leaf size=24 \[ \frac {2 \left (e^{\frac {20+x}{x}}+\left (3-e^{32}\right ) x\right )}{x} \]
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Rubi [A]
time = 0.03, antiderivative size = 28, normalized size of antiderivative = 1.17, number of steps
used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2326}
\begin {gather*} -\frac {40 e^{\frac {x+20}{x}}}{x^3 \left (\frac {1}{x}-\frac {x+20}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {40 e^{\frac {20+x}{x}}}{x^3 \left (\frac {1}{x}-\frac {20+x}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.58 \begin {gather*} \frac {2 e^{1+\frac {20}{x}}}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.39, size = 29, normalized size = 1.21
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
norman | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
risch | \(\frac {2 \,{\mathrm e}^{\frac {20+x}{x}}}{x}\) | \(14\) |
derivativedivides | \(\frac {\left (1+\frac {20}{x}\right ) {\mathrm e}^{1+\frac {20}{x}}}{10}-\frac {{\mathrm e}^{1+\frac {20}{x}}}{10}\) | \(29\) |
default | \(\frac {\left (1+\frac {20}{x}\right ) {\mathrm e}^{1+\frac {20}{x}}}{10}-\frac {{\mathrm e}^{1+\frac {20}{x}}}{10}\) | \(29\) |
meijerg | \(-\frac {{\mathrm e} \left (1-{\mathrm e}^{\frac {20}{x}}\right )}{10}+\frac {{\mathrm e} \left (1-\frac {\left (2-\frac {40}{x}\right ) {\mathrm e}^{\frac {20}{x}}}{2}\right )}{10}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.30, size = 22, normalized size = 0.92 \begin {gather*} -\frac {1}{10} \, e \Gamma \left (2, -\frac {20}{x}\right ) + \frac {1}{10} \, e^{\left (\frac {20}{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 13, normalized size = 0.54 \begin {gather*} \frac {2 \, e^{\left (\frac {x + 20}{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.33 \begin {gather*} \frac {2 e^{\frac {x + 20}{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 27, normalized size = 1.12 \begin {gather*} \frac {{\left (x + 20\right )} e^{\left (\frac {x + 20}{x}\right )}}{10 \, x} - \frac {1}{10} \, e^{\left (\frac {x + 20}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.12, size = 13, normalized size = 0.54 \begin {gather*} \frac {2\,\mathrm {e}\,{\mathrm {e}}^{20/x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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