Optimal. Leaf size=17 \[ e^{3-(2+5 x \log (2))^2} x \]
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Rubi [B] time = 0.06, antiderivative size = 47, normalized size of antiderivative = 2.76, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2288} \begin {gather*} \frac {2^{-20 x} e^{-25 x^2 \log ^2(2)-1} \left (5 x^2 \log ^2(2)+2 x \log (2)\right )}{\log (2) (5 x \log (2)+2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {2^{-20 x} e^{-1-25 x^2 \log ^2(2)} \left (2 x \log (2)+5 x^2 \log ^2(2)\right )}{\log (2) (2+5 x \log (2))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 20, normalized size = 1.18 \begin {gather*} 2^{-20 x} e^{-1-25 x^2 \log ^2(2)} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 19, normalized size = 1.12 \begin {gather*} e^{\left (-25 \, x^{2} \log \relax (2)^{2} - 20 \, x \log \relax (2) + \log \relax (x) - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 19, normalized size = 1.12 \begin {gather*} e^{\left (-25 \, x^{2} \log \relax (2)^{2} - 20 \, x \log \relax (2) + \log \relax (x) - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 18, normalized size = 1.06
method | result | size |
risch | \(x \left (\frac {1}{1048576}\right )^{x} {\mathrm e}^{-1-25 x^{2} \ln \relax (2)^{2}}\) | \(18\) |
gosper | \({\mathrm e}^{\ln \relax (x )-25 x^{2} \ln \relax (2)^{2}-20 x \ln \relax (2)-1}\) | \(20\) |
norman | \({\mathrm e}^{\ln \relax (x )-25 x^{2} \ln \relax (2)^{2}-20 x \ln \relax (2)-1}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.73, size = 323, normalized size = 19.00 \begin {gather*} -\frac {{\left (\frac {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{3} \Gamma \left (\frac {3}{2}, \frac {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}}{\log \relax (2)^{2}}\right ) \log \relax (2)^{3}}{{\left ({\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}\right )}^{\frac {3}{2}} \left (-\log \relax (2)^{2}\right )^{\frac {5}{2}}} - \frac {4 \, \sqrt {\pi } {\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )} {\left (\operatorname {erf}\left (\frac {\sqrt {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}}}{\log \relax (2)}\right ) - 1\right )} \log \relax (2)^{3}}{\sqrt {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}} \left (-\log \relax (2)^{2}\right )^{\frac {5}{2}}} - \frac {4 \, e^{\left (-\frac {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}}{\log \relax (2)^{2}}\right )} \log \relax (2)^{3}}{\left (-\log \relax (2)^{2}\right )^{\frac {5}{2}}}\right )} e^{3} \log \relax (2)^{2}}{5 \, \sqrt {-\log \relax (2)^{2}}} + \frac {2 \, {\left (\frac {2 \, \sqrt {\pi } {\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )} {\left (\operatorname {erf}\left (\frac {\sqrt {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}}}{\log \relax (2)}\right ) - 1\right )} \log \relax (2)^{2}}{\sqrt {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}} \left (-\log \relax (2)^{2}\right )^{\frac {3}{2}}} + \frac {e^{\left (-\frac {{\left (5 \, x \log \relax (2)^{2} + 2 \, \log \relax (2)\right )}^{2}}{\log \relax (2)^{2}}\right )} \log \relax (2)^{2}}{\left (-\log \relax (2)^{2}\right )^{\frac {3}{2}}}\right )} e^{3} \log \relax (2)}{5 \, \sqrt {-\log \relax (2)^{2}}} + \frac {\sqrt {\pi } \operatorname {erf}\left (5 \, x \log \relax (2) + 2\right ) e^{3}}{10 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.01, size = 21, normalized size = 1.24 \begin {gather*} \frac {x\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-25\,x^2\,{\ln \relax (2)}^2}}{2^{20\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 1.29 \begin {gather*} x e^{- 25 x^{2} \log {\relax (2 )}^{2} - 20 x \log {\relax (2 )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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