Optimal. Leaf size=12 \[ e^{e^x} x^5 (2+x) \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.25, number of steps
used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2326}
\begin {gather*} e^{e^x} \left (x^6+2 x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{e^x} \left (2 x^5+x^6\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 12, normalized size = 1.00 \begin {gather*} e^{e^x} x^5 (2+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 11, normalized size = 0.92
method | result | size |
risch | \(\left (2+x \right ) x^{5} {\mathrm e}^{{\mathrm e}^{x}}\) | \(11\) |
norman | \(x^{6} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 1.08 \begin {gather*} {\left (x^{6} + 2 \, x^{5}\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 13, normalized size = 1.08 \begin {gather*} {\left (x^{6} + 2 \, x^{5}\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 12, normalized size = 1.00 \begin {gather*} \left (x^{6} + 2 x^{5}\right ) e^{e^{x}} \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. 25 vs.
\(2 (10) = 20\).
time = 0.40, size = 25, normalized size = 2.08 \begin {gather*} {\left (x^{6} e^{\left (x + e^{x}\right )} + 2 \, x^{5} e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.81, size = 10, normalized size = 0.83 \begin {gather*} x^5\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (x+2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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