Optimal. Leaf size=18 \[ e^{\frac {16 \left (16+e^{e^x}\right ) x}{25 \log ^2(2)}} \]
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Rubi [A] time = 0.14, antiderivative size = 21, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 6706} \begin {gather*} e^{\frac {16 \left (e^{e^x} x+16 x\right )}{25 \log ^2(2)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{\frac {256 x+16 e^{e^x} x}{25 \log ^2(2)}} \left (256+e^{e^x} \left (16+16 e^x x\right )\right ) \, dx}{25 \log ^2(2)}\\ &=e^{\frac {16 \left (16 x+e^{e^x} x\right )}{25 \log ^2(2)}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.50, size = 18, normalized size = 1.00 \begin {gather*} e^{\frac {16 \left (16+e^{e^x}\right ) x}{25 \log ^2(2)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 16, normalized size = 0.89 \begin {gather*} e^{\left (\frac {16 \, {\left (x e^{\left (e^{x}\right )} + 16 \, x\right )}}{25 \, \log \relax (2)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 19, normalized size = 1.06 \begin {gather*} e^{\left (\frac {16 \, x e^{\left (e^{x}\right )}}{25 \, \log \relax (2)^{2}} + \frac {256 \, x}{25 \, \log \relax (2)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 14, normalized size = 0.78
method | result | size |
risch | \({\mathrm e}^{\frac {16 \left ({\mathrm e}^{{\mathrm e}^{x}}+16\right ) x}{25 \ln \relax (2)^{2}}}\) | \(14\) |
norman | \({\mathrm e}^{\frac {16 x \,{\mathrm e}^{{\mathrm e}^{x}}+256 x}{25 \ln \relax (2)^{2}}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 19, normalized size = 1.06 \begin {gather*} e^{\left (\frac {16 \, x e^{\left (e^{x}\right )}}{25 \, \log \relax (2)^{2}} + \frac {256 \, x}{25 \, \log \relax (2)^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.64, size = 17, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^{\frac {256\,x+16\,x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{25\,{\ln \relax (2)}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 20, normalized size = 1.11 \begin {gather*} e^{\frac {\frac {16 x e^{e^{x}}}{25} + \frac {256 x}{25}}{\log {\relax (2 )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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