Optimal. Leaf size=18 \[ \frac {e^{e^x} \left (-17+e^2-x\right )}{\log (3)} \]
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Rubi [A]
time = 0.02, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps
used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2326}
\begin {gather*} -\frac {e^{e^x} \left (x-e^2+17\right )}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{e^x} \left (-1+e^x \left (-17+e^2-x\right )\right ) \, dx}{\log (3)}\\ &=-\frac {e^{e^x} \left (17-e^2+x\right )}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} \frac {e^{e^x} \left (-17+e^2-x\right )}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.52, size = 16, normalized size = 0.89
method | result | size |
risch | \(\frac {\left ({\mathrm e}^{2}-x -17\right ) {\mathrm e}^{{\mathrm e}^{x}}}{\ln \left (3\right )}\) | \(16\) |
norman | \(\frac {\left ({\mathrm e}^{2}-17\right ) {\mathrm e}^{{\mathrm e}^{x}}}{\ln \left (3\right )}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{\ln \left (3\right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 16, normalized size = 0.89 \begin {gather*} -\frac {{\left (x - e^{2} + 17\right )} e^{\left (e^{x}\right )}}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 0.78 \begin {gather*} \frac {\left (- x - 17 + e^{2}\right ) e^{e^{x}}}{\log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 33 vs.
\(2 (16) = 32\).
time = 0.42, size = 33, normalized size = 1.83 \begin {gather*} -\frac {{\left (x e^{\left (x + e^{x}\right )} - e^{\left (x + e^{x} + 2\right )} + 17 \, e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 16, normalized size = 0.89 \begin {gather*} -\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (x-{\mathrm {e}}^2+17\right )}{\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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