Optimal. Leaf size=17 \[ e^{-2+e^x} (3+2 x)^4 \log (9) \]
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Rubi [A]
time = 0.04, antiderivative size = 30, normalized size of antiderivative = 1.76, number of steps
used = 1, number of rules used = 1, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2326}
\begin {gather*} e^{e^x-2} \left (16 x^4+96 x^3+216 x^2+216 x+81\right ) \log (9) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-2+e^x} \left (81+216 x+216 x^2+96 x^3+16 x^4\right ) \log (9)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} e^{-2+e^x} (3+2 x)^4 \log (9) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.46, size = 30, normalized size = 1.76
method | result | size |
risch | \(2 \left (16 x^{4}+96 x^{3}+216 x^{2}+216 x +81\right ) \ln \left (3\right ) {\mathrm e}^{{\mathrm e}^{x}-2}\) | \(30\) |
norman | \(162 \,{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{-2} \ln \left (3\right )+432 \,{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{-2} x \ln \left (3\right )+432 \,{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{-2} x^{2} \ln \left (3\right )+192 \,{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{-2} x^{3} \ln \left (3\right )+32 \,{\mathrm e}^{-2} \ln \left (3\right ) x^{4} {\mathrm e}^{{\mathrm e}^{x}}\) | \(67\) |
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 = 0.37, size = 29, normalized size = 1.71 \begin {gather*} 2 \, {\left (16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right )} e^{\left (e^{x} - 2\right )} \log \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (19) = 38\).
time = 0.13, size = 44, normalized size = 2.59 \begin {gather*} \frac {\left (32 x^{4} \log {\left (3 \right )} + 192 x^{3} \log {\left (3 \right )} + 432 x^{2} \log {\left (3 \right )} + 432 x \log {\left (3 \right )} + 162 \log {\left (3 \right )}\right ) e^{e^{x}}}{e^{2}} \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. 64 vs.
\(2 (16) = 32\).
time = 0.45, size = 64, normalized size = 3.76 \begin {gather*} 2 \, {\left (16 \, x^{4} e^{\left (x + e^{x}\right )} \log \left (3\right ) + 96 \, x^{3} e^{\left (x + e^{x}\right )} \log \left (3\right ) + 216 \, x^{2} e^{\left (x + e^{x}\right )} \log \left (3\right ) + 216 \, x e^{\left (x + e^{x}\right )} \log \left (3\right ) + 81 \, e^{\left (x + e^{x}\right )} \log \left (3\right )\right )} e^{\left (-x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.28, size = 16, normalized size = 0.94 \begin {gather*} 2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-2}\,\ln \left (3\right )\,{\left (2\,x+3\right )}^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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