Optimal. Leaf size=28 \[ e^{x+2 \left (x+2 \left (e^{8 x-x \log (x)}-x\right )^2 x\right )} \]
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Rubi [A] time = 2.14, antiderivative size = 39, normalized size of antiderivative = 1.39, number of steps used = 1, number of rules used = 1, integrand size = 99, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6706} \begin {gather*} \exp \left (4 e^{16 x} x^{1-2 x}-8 e^{8 x} x^{2-x}+4 x^3+3 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (3 x+4 x^3+4 e^{16 x} x^{1-2 x}-8 e^{8 x} x^{2-x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 39, normalized size = 1.39 \begin {gather*} e^{3 x+4 x^3+4 e^{16 x} x^{1-2 x}-8 e^{8 x} x^{2-x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 38, normalized size = 1.36 \begin {gather*} e^{\left (4 \, x^{3} - 8 \, x^{2} e^{\left (-x \log \relax (x) + 8 \, x\right )} + 4 \, x e^{\left (-2 \, x \log \relax (x) + 16 \, x\right )} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.73, size = 38, normalized size = 1.36 \begin {gather*} e^{\left (4 \, x^{3} - 8 \, x^{2} e^{\left (-x \log \relax (x) + 8 \, x\right )} + 4 \, x e^{\left (-2 \, x \log \relax (x) + 16 \, x\right )} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 36, normalized size = 1.29
method | result | size |
risch | \({\mathrm e}^{x \left (4 x^{-2 x} {\mathrm e}^{16 x}-8 x^{-x} {\mathrm e}^{8 x} x +4 x^{2}+3\right )}\) | \(36\) |
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*} \int {\left (12 \, x^{2} + 8 \, {\left (x^{2} \log \relax (x) - 7 \, x^{2} - 2 \, x\right )} e^{\left (-x \log \relax (x) + 8 \, x\right )} - 4 \, {\left (2 \, x \log \relax (x) - 14 \, x - 1\right )} e^{\left (-2 \, x \log \relax (x) + 16 \, x\right )} + 3\right )} e^{\left (4 \, x^{3} - 8 \, x^{2} e^{\left (-x \log \relax (x) + 8 \, x\right )} + 4 \, x e^{\left (-2 \, x \log \relax (x) + 16 \, x\right )} + 3 \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.22, size = 39, normalized size = 1.39 \begin {gather*} {\mathrm {e}}^{-8\,x^{2-x}\,{\mathrm {e}}^{8\,x}}\,{\mathrm {e}}^{4\,x^{1-2\,x}\,{\mathrm {e}}^{16\,x}}\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{4\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.91, size = 39, normalized size = 1.39 \begin {gather*} e^{4 x^{3} - 8 x^{2} e^{- x \log {\relax (x )} + 8 x} + 4 x e^{- 2 x \log {\relax (x )} + 16 x} + 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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