Optimal. Leaf size=22 \[ e^{4 e^6 x \left (\frac {e^x}{2}+x-x^2\right )} \]
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Rubi [A] time = 0.14, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6706} \begin {gather*} e^{4 e^6 \left (x^2-x^3\right )+2 e^{x+6} x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{2 e^{6+x} x+4 e^6 \left (x^2-x^3\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 18, normalized size = 0.82 \begin {gather*} e^{2 e^6 x \left (e^x-2 (-1+x) x\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 22, normalized size = 1.00 \begin {gather*} e^{\left (-4 \, {\left (x^{3} - x^{2}\right )} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 24, normalized size = 1.09
method | result | size |
norman | \({\mathrm e}^{2 x \,{\mathrm e}^{6} {\mathrm e}^{x}+\left (-4 x^{3}+4 x^{2}\right ) {\mathrm e}^{6}}\) | \(24\) |
risch | \({\mathrm e}^{-2 x \left (2 x^{2} {\mathrm e}^{6}-2 x \,{\mathrm e}^{6}-{\mathrm e}^{x +6}\right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.35, size = 25, normalized size = 1.14 \begin {gather*} {\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^6}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 24, normalized size = 1.09 \begin {gather*} e^{2 x e^{6} e^{x} + \left (- 4 x^{3} + 4 x^{2}\right ) e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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