Optimal. Leaf size=21 \[ 25+\frac {e^{\frac {1}{4}+5 \left (-5+e^{e^x}\right )}}{x} \]
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Rubi [A]
time = 0.09, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps
used = 1, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {2326}
\begin {gather*} \frac {e^{\frac {1}{4} \left (20 e^{e^x}-99\right )}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{\frac {1}{4} \left (-99+20 e^{e^x}\right )}}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 0.81 \begin {gather*} \frac {e^{-\frac {99}{4}+5 e^{e^x}}}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 13, normalized size = 0.62
method | result | size |
norman | \(\frac {{\mathrm e}^{5 \,{\mathrm e}^{{\mathrm e}^{x}}-\frac {99}{4}}}{x}\) | \(13\) |
risch | \(\frac {{\mathrm e}^{5 \,{\mathrm e}^{{\mathrm e}^{x}}-\frac {99}{4}}}{x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 12, normalized size = 0.57 \begin {gather*} \frac {e^{\left (5 \, e^{\left (e^{x}\right )} - \frac {99}{4}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 23, normalized size = 1.10 \begin {gather*} \frac {e^{\left (\frac {1}{4} \, {\left (20 \, e^{\left (x + e^{x}\right )} - 99 \, e^{x}\right )} e^{\left (-x\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 12, normalized size = 0.57 \begin {gather*} \frac {e^{5 e^{e^{x}} - \frac {99}{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 = 3.26, size = 12, normalized size = 0.57 \begin {gather*} \frac {{\mathrm {e}}^{5\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {99}{4}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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