Optimal. Leaf size=25 \[ 2 e^{25 (-1+x)^2+\frac {2}{5+\log (3) \log ^2(4)}} \]
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Rubi [A]
time = 0.36, antiderivative size = 38, normalized size of antiderivative = 1.52, number of steps
used = 2, number of rules used = 2, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2276, 2268}
\begin {gather*} \exp \left (25 x^2-50 x+\frac {127+(25+\log (2)) \log (3) \log ^2(4)+\log (32)}{5+\log (3) \log ^2(4)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2268
Rule 2276
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (-50 x+25 x^2+\frac {127+(25+\log (2)) \log (3) \log ^2(4)+\log (32)}{5+\log (3) \log ^2(4)}\right ) (-50+50 x) \, dx\\ &=\exp \left (-50 x+25 x^2+\frac {127+(25+\log (2)) \log (3) \log ^2(4)+\log (32)}{5+\log (3) \log ^2(4)}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(76\) vs. \(2(25)=50\).
time = 0.65, size = 76, normalized size = 3.04 \begin {gather*} \frac {e^{\frac {127+(25+\log (2)) \log (3) \log ^2(4)-50 x \left (5+\log (3) \log ^2(4)\right )+25 x^2 \left (5+\log (3) \log ^2(4)\right )+\log (32)}{5+\log (3) \log ^2(4)}} \left (5+\log ^2(2) \log (81)\right )}{5+\log (3) \log ^2(4)} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 497, normalized size = 19.88
method | result | size |
norman | \({\mathrm e}^{\frac {4 \left (\ln \left (2\right )+25 x^{2}-50 x +25\right ) \ln \left (3\right ) \ln \left (2\right )^{2}+5 \ln \left (2\right )+125 x^{2}-250 x +127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}\) | \(49\) |
gosper | \({\mathrm e}^{\frac {100 x^{2} \ln \left (3\right ) \ln \left (2\right )^{2}+4 \ln \left (3\right ) \ln \left (2\right )^{3}-200 \ln \left (2\right )^{2} \ln \left (3\right ) x +100 \ln \left (2\right )^{2} \ln \left (3\right )+125 x^{2}+5 \ln \left (2\right )-250 x +127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}\) | \(65\) |
risch | \({\mathrm e}^{\frac {100 x^{2} \ln \left (3\right ) \ln \left (2\right )^{2}+4 \ln \left (3\right ) \ln \left (2\right )^{3}-200 \ln \left (2\right )^{2} \ln \left (3\right ) x +100 \ln \left (2\right )^{2} \ln \left (3\right )+125 x^{2}+5 \ln \left (2\right )-250 x +127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}\) | \(65\) |
default | \(\frac {25 \left (4 \ln \left (2\right )^{2} \ln \left (3\right )+5\right ) {\mathrm e}^{\frac {\left (100 \ln \left (2\right )^{2} \ln \left (3\right )+125\right ) x^{2}}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}+\frac {\left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right ) x}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}+\frac {4 \left (\ln \left (2\right )+25\right ) \ln \left (3\right ) \ln \left (2\right )^{2}+5 \ln \left (2\right )+127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}}{100 \ln \left (2\right )^{2} \ln \left (3\right )+125}+\frac {25 i \left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right ) \sqrt {\pi }\, {\mathrm e}^{\frac {4 \left (\ln \left (2\right )+25\right ) \ln \left (3\right ) \ln \left (2\right )^{2}+5 \ln \left (2\right )+127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}-\frac {\left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right )^{2}}{4 \left (4 \ln \left (2\right )^{2} \ln \left (3\right )+5\right ) \left (100 \ln \left (2\right )^{2} \ln \left (3\right )+125\right )}} \erf \left (i \sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}\, x +\frac {i \left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right )}{2 \left (4 \ln \left (2\right )^{2} \ln \left (3\right )+5\right ) \sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}}\right )}{2 \left (100 \ln \left (2\right )^{2} \ln \left (3\right )+125\right ) \sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}}+\frac {25 i \sqrt {\pi }\, {\mathrm e}^{\frac {4 \left (\ln \left (2\right )+25\right ) \ln \left (3\right ) \ln \left (2\right )^{2}+5 \ln \left (2\right )+127}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}-\frac {\left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right )^{2}}{4 \left (4 \ln \left (2\right )^{2} \ln \left (3\right )+5\right ) \left (100 \ln \left (2\right )^{2} \ln \left (3\right )+125\right )}} \erf \left (i \sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}\, x +\frac {i \left (-200 \ln \left (2\right )^{2} \ln \left (3\right )-250\right )}{2 \left (4 \ln \left (2\right )^{2} \ln \left (3\right )+5\right ) \sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}}\right )}{\sqrt {\frac {100 \ln \left (2\right )^{2} \ln \left (3\right )+125}{4 \ln \left (2\right )^{2} \ln \left (3\right )+5}}}\) | \(497\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.57, size = 200, normalized size = 8.00 \begin {gather*} 10 i \, \sqrt {\pi } 3^{\frac {4 \, \log \left (2\right )^{3}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {100 \, \log \left (2\right )^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5}} 2^{\frac {5}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} - 1} \operatorname {erf}\left (5 i \, x - 5 i\right ) e^{\left (\frac {127}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} - 25\right )} + {\left (\frac {5 \, \sqrt {\pi } {\left (x - 1\right )} {\left (\operatorname {erf}\left (5 \, \sqrt {-{\left (x - 1\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (x - 1\right )}^{2}}} + e^{\left (25 \, {\left (x - 1\right )}^{2}\right )}\right )} e^{\left (\frac {4 \, \log \left (3\right ) \log \left (2\right )^{3}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {100 \, \log \left (3\right ) \log \left (2\right )^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {5 \, \log \left (2\right )}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {127}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} - 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (25) = 50\).
time = 0.39, size = 51, normalized size = 2.04 \begin {gather*} e^{\left (\frac {125 \, x^{2} + 4 \, {\left (25 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} + \log \left (2\right )^{3}\right )} \log \left (3\right ) - 250 \, x + 5 \, \log \left (2\right ) + 127}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (22) = 44\).
time = 0.06, size = 51, normalized size = 2.04 \begin {gather*} e^{\frac {125 x^{2} - 250 x + \left (100 x^{2} - 200 x + 4 \log {\left (2 \right )} + 100\right ) \log {\left (2 \right )}^{2} \log {\left (3 \right )} + 5 \log {\left (2 \right )} + 127}{4 \log {\left (2 \right )}^{2} \log {\left (3 \right )} + 5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs.
\(2 (25) = 50\).
time = 0.43, size = 148, normalized size = 5.92 \begin {gather*} e^{\left (\frac {100 \, x^{2} \log \left (3\right ) \log \left (2\right )^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} - \frac {200 \, x \log \left (3\right ) \log \left (2\right )^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {4 \, \log \left (3\right ) \log \left (2\right )^{3}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {100 \, \log \left (3\right ) \log \left (2\right )^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {125 \, x^{2}}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} - \frac {250 \, x}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {5 \, \log \left (2\right )}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5} + \frac {127}{4 \, \log \left (3\right ) \log \left (2\right )^{2} + 5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.33, size = 106, normalized size = 4.24 \begin {gather*} {32}^{\frac {1}{4\,{\ln \left (2\right )}^2\,\ln \left (3\right )+5}}\,{81}^{\frac {25\,{\ln \left (2\right )}^2\,x^2-50\,{\ln \left (2\right )}^2\,x+25\,{\ln \left (2\right )}^2+{\ln \left (2\right )}^3}{4\,{\ln \left (2\right )}^2\,\ln \left (3\right )+5}}\,{\mathrm {e}}^{\frac {127}{4\,{\ln \left (2\right )}^2\,\ln \left (3\right )+5}}\,{\mathrm {e}}^{-\frac {250\,x}{4\,{\ln \left (2\right )}^2\,\ln \left (3\right )+5}}\,{\mathrm {e}}^{\frac {125\,x^2}{4\,{\ln \left (2\right )}^2\,\ln \left (3\right )+5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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