Optimal. Leaf size=31 \[ e^{x^2 \left (2 \left (3+e^{\frac {x^2}{e}}\right )-x+x \log ^2(25)\right )^2} \]
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Rubi [A]
time = 7.20, antiderivative size = 59, normalized size of antiderivative = 1.90, number of steps
used = 3, number of rules used = 3, integrand size = 201, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6820, 12,
6838} \begin {gather*} \exp \left (x^4 \left (1-\log ^2(25)\right )^2+4 \left (e^{\frac {x^2}{e}}+3\right )^2 x^2-4 \left (e^{\frac {x^2}{e}}+3\right ) x^3 \left (1-\log ^2(25)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 4 \exp \left (-1+4 \left (3+e^{\frac {x^2}{e}}\right )^2 x^2+4 \left (3+e^{\frac {x^2}{e}}\right ) x^3 \left (-1+\log ^2(25)\right )+x^4 \left (-1+\log ^2(25)\right )^2\right ) x \left (6+2 e^{\frac {x^2}{e}}+x \left (-1+\log ^2(25)\right )\right ) \left (e^{1+\frac {x^2}{e}}+2 e^{\frac {x^2}{e}} x^2+e \left (3+x \left (-1+\log ^2(25)\right )\right )\right ) \, dx\\ &=4 \int \exp \left (-1+4 \left (3+e^{\frac {x^2}{e}}\right )^2 x^2+4 \left (3+e^{\frac {x^2}{e}}\right ) x^3 \left (-1+\log ^2(25)\right )+x^4 \left (-1+\log ^2(25)\right )^2\right ) x \left (6+2 e^{\frac {x^2}{e}}+x \left (-1+\log ^2(25)\right )\right ) \left (e^{1+\frac {x^2}{e}}+2 e^{\frac {x^2}{e}} x^2+e \left (3+x \left (-1+\log ^2(25)\right )\right )\right ) \, dx\\ &=\exp \left (4 \left (3+e^{\frac {x^2}{e}}\right )^2 x^2-4 \left (3+e^{\frac {x^2}{e}}\right ) x^3 \left (1-\log ^2(25)\right )+x^4 \left (1-\log ^2(25)\right )^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.24, size = 29, normalized size = 0.94 \begin {gather*} e^{x^2 \left (6+2 e^{\frac {x^2}{e}}+x \left (-1+\log ^2(25)\right )\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs.
\(2(30)=60\).
time = 4.81, size = 82, normalized size = 2.65
method | result | size |
risch | \({\mathrm e}^{x^{2} \left (16 \ln \left (5\right )^{4} x^{2}+16 \ln \left (5\right )^{2} {\mathrm e}^{x^{2} {\mathrm e}^{-1}} x -8 x^{2} \ln \left (5\right )^{2}+48 x \ln \left (5\right )^{2}-4 \,{\mathrm e}^{x^{2} {\mathrm e}^{-1}} x +x^{2}+4 \,{\mathrm e}^{2 x^{2} {\mathrm e}^{-1}}+24 \,{\mathrm e}^{x^{2} {\mathrm e}^{-1}}-12 x +36\right )}\) | \(82\) |
norman | \({\mathrm e}^{4 x^{2} {\mathrm e}^{2 x^{2} {\mathrm e}^{-1}}+\left (16 x^{3} \ln \left (5\right )^{2}-4 x^{3}+24 x^{2}\right ) {\mathrm e}^{x^{2} {\mathrm e}^{-1}}+16 x^{4} \ln \left (5\right )^{4}+4 \left (-2 x^{4}+12 x^{3}\right ) \ln \left (5\right )^{2}+x^{4}-12 x^{3}+36 x^{2}}\) | \(88\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 95 vs.
\(2 (28) = 56\).
time = 0.75, size = 95, normalized size = 3.06 \begin {gather*} e^{\left (16 \, x^{4} \log \left (5\right )^{4} - 8 \, x^{4} \log \left (5\right )^{2} + 16 \, x^{3} e^{\left (x^{2} e^{\left (-1\right )}\right )} \log \left (5\right )^{2} + 48 \, x^{3} \log \left (5\right )^{2} + x^{4} - 4 \, x^{3} e^{\left (x^{2} e^{\left (-1\right )}\right )} - 12 \, x^{3} + 4 \, x^{2} e^{\left (2 \, x^{2} e^{\left (-1\right )}\right )} + 24 \, x^{2} e^{\left (x^{2} e^{\left (-1\right )}\right )} + 36 \, x^{2}\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. 81 vs.
\(2 (28) = 56\).
time = 0.37, size = 81, normalized size = 2.61 \begin {gather*} e^{\left (16 \, x^{4} \log \left (5\right )^{4} + x^{4} - 12 \, x^{3} + 4 \, x^{2} e^{\left (2 \, x^{2} e^{\left (-1\right )}\right )} - 8 \, {\left (x^{4} - 6 \, x^{3}\right )} \log \left (5\right )^{2} + 36 \, x^{2} + 4 \, {\left (4 \, x^{3} \log \left (5\right )^{2} - x^{3} + 6 \, x^{2}\right )} e^{\left (x^{2} e^{\left (-1\right )}\right )}\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. 83 vs.
\(2 (27) = 54\).
time = 0.47, size = 83, normalized size = 2.68 \begin {gather*} e^{x^{4} + 16 x^{4} \log {\left (5 \right )}^{4} - 12 x^{3} + 4 x^{2} e^{\frac {2 x^{2}}{e}} + 36 x^{2} + \left (- 8 x^{4} + 48 x^{3}\right ) \log {\left (5 \right )}^{2} + \left (- 4 x^{3} + 16 x^{3} \log {\left (5 \right )}^{2} + 24 x^{2}\right ) e^{\frac {x^{2}}{e}}} \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. 95 vs.
\(2 (28) = 56\).
time = 0.89, size = 95, normalized size = 3.06 \begin {gather*} e^{\left (16 \, x^{4} \log \left (5\right )^{4} - 8 \, x^{4} \log \left (5\right )^{2} + 16 \, x^{3} e^{\left (x^{2} e^{\left (-1\right )}\right )} \log \left (5\right )^{2} + 48 \, x^{3} \log \left (5\right )^{2} + x^{4} - 4 \, x^{3} e^{\left (x^{2} e^{\left (-1\right )}\right )} - 12 \, x^{3} + 4 \, x^{2} e^{\left (2 \, x^{2} e^{\left (-1\right )}\right )} + 24 \, x^{2} e^{\left (x^{2} e^{\left (-1\right )}\right )} + 36 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.97, size = 104, normalized size = 3.35 \begin {gather*} {\mathrm {e}}^{x^4}\,{\mathrm {e}}^{-8\,x^4\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{16\,x^4\,{\ln \left (5\right )}^4}\,{\mathrm {e}}^{48\,x^3\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{16\,x^3\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{-1}}\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{-12\,x^3}\,{\mathrm {e}}^{36\,x^2}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{-1}}}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^{-1}}}\,{\mathrm {e}}^{24\,x^2\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{-1}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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