Optimal. Leaf size=15 \[ e^{2+x} x^{-\frac {1}{\log (\log (x))}} \]
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Rubi [A]
time = 0.14, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6820, 2326}
\begin {gather*} e^{x+2} x^{-\frac {1}{\log (\log (x))}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2+x} x^{-1-\frac {1}{\log (\log (x))}} \left (1-\log (\log (x))+x \log ^2(\log (x))\right )}{\log ^2(\log (x))} \, dx\\ &=e^{2+x} x^{-\frac {1}{\log (\log (x))}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 15, normalized size = 1.00 \begin {gather*} e^{2+x} x^{-\frac {1}{\log (\log (x))}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 15, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{2+x} x^{-\frac {1}{\ln \left (\ln \left (x \right )\right )}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 14, normalized size = 0.93 \begin {gather*} \frac {e^{\left (x + 2\right )}}{x^{\left (\frac {1}{\log \left (\log \left (x\right )\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 17.31, size = 15, normalized size = 1.00 \begin {gather*} e^{2} e^{x} e^{- \frac {\log {\left (x \right )}}{\log {\left (\log {\left (x \right )} \right )}}} \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 = 5.55, size = 14, normalized size = 0.93 \begin {gather*} \frac {{\mathrm {e}}^2\,{\mathrm {e}}^x}{x^{\frac {1}{\ln \left (\ln \left (x\right )\right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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