Optimal. Leaf size=31 \[ 4-e^{1-e^x \left (2 x-e^{x+e^{4 x} x} x\right )} \]
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Rubi [A] time = 0.38, antiderivative size = 27, normalized size of antiderivative = 0.87, number of steps used = 1, number of rules used = 1, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6706} \begin {gather*} -e^{-2 e^x x+e^{e^{4 x} x+2 x} x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-e^{1-2 e^x x+e^{2 x+e^{4 x} x} x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 2.92, size = 27, normalized size = 0.87 \begin {gather*} -e^{1-2 e^x x+e^{2 x+e^{4 x} x} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 23, normalized size = 0.74 \begin {gather*} -e^{\left (x e^{\left (x e^{\left (4 \, x\right )} + 2 \, x\right )} - 2 \, x e^{x} + 1\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 ({\left ({\left (4 \, x^{2} + x\right )} e^{\left (5 \, x\right )} + {\left (2 \, x + 1\right )} e^{x}\right )} e^{\left (x e^{\left (4 \, x\right )} + x\right )} - 2 \, {\left (x + 1\right )} e^{x}\right )} e^{\left (x e^{\left (x e^{\left (4 \, x\right )} + 2 \, x\right )} - 2 \, x e^{x} + 1\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 0.71
method | result | size |
risch | \(-{\mathrm e}^{x \,{\mathrm e}^{x \left (2+{\mathrm e}^{4 x}\right )}-2 \,{\mathrm e}^{x} x +1}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 23, normalized size = 0.74 \begin {gather*} -e^{\left (x e^{\left (x e^{\left (4 \, x\right )} + 2 \, x\right )} - 2 \, x e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.30, size = 24, normalized size = 0.77 \begin {gather*} -{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^x}\,\mathrm {e}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{4\,x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.82, size = 26, normalized size = 0.84 \begin {gather*} - e^{x e^{x} e^{x e^{4 x} + x} - 2 x e^{x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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