Optimal. Leaf size=23 \[ \frac {1}{2} e^{-2+2 e^{4 e^x}-2 x} x^4 \]
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Rubi [B] time = 0.16, antiderivative size = 56, normalized size of antiderivative = 2.43, number of steps used = 1, number of rules used = 1, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {2288} \begin {gather*} \frac {e^{-2 x+2 e^{4 e^x}-2} x^2 \left (x^2-4 e^{x+4 e^x} x^2\right )}{2 \left (1-4 e^{x+4 e^x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-2+2 e^{4 e^x}-2 x} x^2 \left (x^2-4 e^{4 e^x+x} x^2\right )}{2 \left (1-4 e^{4 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}{2} e^{-2+2 e^{4 e^x}-2 x} x^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 34, normalized size = 1.48 \begin {gather*} \frac {1}{2} \, x^{2} e^{\left (-2 \, {\left ({\left (x + 1\right )} e^{x} - e^{x} \log \relax (x) - e^{\left (x + 4 \, e^{x}\right )}\right )} e^{\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*} \int {\left (4 \, x^{2} e^{\left (x + 4 \, e^{x}\right )} - x^{2} + 2 \, x\right )} e^{\left (-2 \, x + 2 \, e^{\left (4 \, e^{x}\right )} + 2 \, \log \relax (x) - 2\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 19, normalized size = 0.83
method | result | size |
risch | \(\frac {x^{4} {\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{x}}-2-2 x}}{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 18, normalized size = 0.78 \begin {gather*} \frac {1}{2} \, x^{4} e^{\left (-2 \, x + 2 \, e^{\left (4 \, e^{x}\right )} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.68, size = 19, normalized size = 0.83 \begin {gather*} \frac {x^4\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^x}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 22.55, size = 20, normalized size = 0.87 \begin {gather*} \frac {x^{4} e^{- 2 x} e^{2 e^{4 e^{x}} - 2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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