Optimal. Leaf size=23 \[ \frac {1}{9} e^{3^{e^{-x} x}+x} x^2 (1+x) \]
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Rubi [A]
time = 0.05, antiderivative size = 40, normalized size of antiderivative = 1.74, number of steps
used = 2, number of rules used = 2, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {12, 2326}
\begin {gather*} \frac {e^{3^{e^{-x} x}} \left (x^2-x^4\right )}{9 \left (e^{-x}-e^{-x} x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int e^{3^{e^{-x} x}} \left (e^x \left (2 x+4 x^2+x^3\right )+3^{e^{-x} x} \left (x^2-x^4\right ) \log (3)\right ) \, dx\\ &=\frac {e^{3^{e^{-x} x}} \left (x^2-x^4\right )}{9 \left (e^{-x}-e^{-x} x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 23, normalized size = 1.00 \begin {gather*} \frac {1}{9} e^{3^{e^{-x} x}+x} x^2 (1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 20, normalized size = 0.87
method | result | size |
risch | \(\frac {\left (x +1\right ) x^{2} {\mathrm e}^{x +3^{x \,{\mathrm e}^{-x}}}}{9}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.66, size = 20, normalized size = 0.87 \begin {gather*} \frac {1}{9} \, {\left (x^{3} + x^{2}\right )} e^{\left (3^{x e^{\left (-x\right )}} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 20, normalized size = 0.87 \begin {gather*} \frac {1}{9} \, {\left (x^{3} + x^{2}\right )} e^{\left (3^{x e^{\left (-x\right )}} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.97, size = 26, normalized size = 1.13 \begin {gather*} \frac {\left (x^{3} e^{x} + x^{2} e^{x}\right ) e^{e^{x e^{- x} \log {\left (3 \right )}}}}{9} \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 = 4.59, size = 19, normalized size = 0.83 \begin {gather*} \frac {x^2\,{\mathrm {e}}^{3^{x\,{\mathrm {e}}^{-x}}}\,{\mathrm {e}}^x\,\left (x+1\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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