Optimal. Leaf size=22 \[ e^{2 x^2 \left (-2 e^{625/x}+x\right )}-x \]
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Rubi [A] time = 0.11, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 2, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6706} \begin {gather*} e^{2 x^3-4 e^{625/x} x^2}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{-2 e^{\frac {625+x \log (2)}{x}} x^2+2 x^3} \left (e^{\frac {625+x \log (2)}{x}} (1250-4 x)+6 x^2\right ) \, dx\\ &=e^{-4 e^{625/x} x^2+2 x^3}-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.23, size = 24, normalized size = 1.09 \begin {gather*} e^{-4 e^{625/x} x^2+2 x^3}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 27, normalized size = 1.23 \begin {gather*} -x + e^{\left (2 \, x^{3} - 2 \, x^{2} e^{\left (\frac {x \log \relax (2) + 625}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 25, normalized size = 1.14 \begin {gather*} -x + e^{\left (2 \, x^{3} - 2 \, x^{2} e^{\left (\frac {625}{x} + \log \relax (2)\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 21, normalized size = 0.95
method | result | size |
risch | \(-x +{\mathrm e}^{2 x^{2} \left (-2 \,{\mathrm e}^{\frac {625}{x}}+x \right )}\) | \(21\) |
default | \(-x +{\mathrm e}^{-2 x^{2} {\mathrm e}^{\frac {x \ln \relax (2)+625}{x}}+2 x^{3}}\) | \(28\) |
norman | \(-x +{\mathrm e}^{-2 x^{2} {\mathrm e}^{\frac {x \ln \relax (2)+625}{x}}+2 x^{3}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 22, normalized size = 1.00 \begin {gather*} -x + e^{\left (2 \, x^{3} - 4 \, x^{2} e^{\frac {625}{x}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.38, size = 23, normalized size = 1.05 \begin {gather*} {\mathrm {e}}^{-4\,x^2\,{\mathrm {e}}^{625/x}}\,{\mathrm {e}}^{2\,x^3}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 22, normalized size = 1.00 \begin {gather*} - x + e^{2 x^{3} - 2 x^{2} e^{\frac {x \log {\relax (2 )} + 625}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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