Optimal. Leaf size=26 \[ -3+e^{4 \left (-\log ^2(2)+(-2+x) x^3 (5 x+\log (2))\right )} \]
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Rubi [A] time = 0.19, antiderivative size = 33, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 1, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6706} \begin {gather*} 2^{4 x^4-8 x^3} e^{20 x^5-40 x^4-4 \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2^{-8 x^3+4 x^4} e^{-40 x^4+20 x^5-4 \log ^2(2)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.58, size = 30, normalized size = 1.15 \begin {gather*} 2^{4 (-2+x) x^3} e^{-40 x^4+20 x^5-4 \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 31, normalized size = 1.19 \begin {gather*} e^{\left (20 \, x^{5} - 40 \, x^{4} + 4 \, {\left (x^{4} - 2 \, x^{3}\right )} \log \relax (2) - 4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 32, normalized size = 1.23 \begin {gather*} e^{\left (20 \, x^{5} + 4 \, x^{4} \log \relax (2) - 40 \, x^{4} - 8 \, x^{3} \log \relax (2) - 4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 29, normalized size = 1.12
method | result | size |
risch | \(16^{\left (x -2\right ) x^{3}} {\mathrm e}^{-4 \ln \relax (2)^{2}+20 x^{5}-40 x^{4}}\) | \(29\) |
gosper | \({\mathrm e}^{4 x^{4} \ln \relax (2)+20 x^{5}-8 x^{3} \ln \relax (2)-40 x^{4}-4 \ln \relax (2)^{2}}\) | \(33\) |
derivativedivides | \({\mathrm e}^{-4 \ln \relax (2)^{2}+\left (4 x^{4}-8 x^{3}\right ) \ln \relax (2)+20 x^{5}-40 x^{4}}\) | \(33\) |
default | \({\mathrm e}^{-4 \ln \relax (2)^{2}+\left (4 x^{4}-8 x^{3}\right ) \ln \relax (2)+20 x^{5}-40 x^{4}}\) | \(33\) |
norman | \({\mathrm e}^{-4 \ln \relax (2)^{2}+\left (4 x^{4}-8 x^{3}\right ) \ln \relax (2)+20 x^{5}-40 x^{4}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 32, normalized size = 1.23 \begin {gather*} e^{\left (20 \, x^{5} + 4 \, x^{4} \log \relax (2) - 40 \, x^{4} - 8 \, x^{3} \log \relax (2) - 4 \, \log \relax (2)^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.35, size = 36, normalized size = 1.38 \begin {gather*} \frac {2^{4\,x^4}\,{\mathrm {e}}^{-4\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{20\,x^5}\,{\mathrm {e}}^{-40\,x^4}}{2^{8\,x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 31, normalized size = 1.19 \begin {gather*} e^{20 x^{5} - 40 x^{4} + \left (4 x^{4} - 8 x^{3}\right ) \log {\relax (2 )} - 4 \log {\relax (2 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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