Optimal. Leaf size=21 \[ e^{\left (-x+3 (-e+2 x)^2 \log (5)\right )^2} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(21)=42\).
time = 0.38, antiderivative size = 62, normalized size of antiderivative = 2.95, number of steps
used = 1, number of rules used = 1, integrand size = 114, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {6838}
\begin {gather*} 5^{-24 x^3+24 e x^2-6 e^2 x} \exp \left (x^2+9 \left (16 x^4-32 e x^3+24 e^2 x^2-8 e^3 x+e^4\right ) \log ^2(5)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5^{-6 e^2 x+24 e x^2-24 x^3} \exp \left (x^2+9 \left (e^4-8 e^3 x+24 e^2 x^2-32 e x^3+16 x^4\right ) \log ^2(5)\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(21)=42\).
time = 1.19, size = 51, normalized size = 2.43 \begin {gather*} 5^{-6 (e-2 x)^2 x} e^{\frac {1}{4} \left (e^2-2 e (e-2 x)+(e-2 x)^2+36 (e-2 x)^4 \log ^2(5)\right )} \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. \(68\) vs.
\(2(21)=42\).
time = 0.93, size = 69, normalized size = 3.29
method | result | size |
derivativedivides | \({\mathrm e}^{\left (9 \,{\mathrm e}^{4}-72 x \,{\mathrm e}^{3}+216 x^{2} {\mathrm e}^{2}-288 x^{3} {\mathrm e}+144 x^{4}\right ) \ln \left (5\right )^{2}+\left (-6 \,{\mathrm e}^{2} x +24 x^{2} {\mathrm e}-24 x^{3}\right ) \ln \left (5\right )+x^{2}}\) | \(69\) |
default | \({\mathrm e}^{\left (9 \,{\mathrm e}^{4}-72 x \,{\mathrm e}^{3}+216 x^{2} {\mathrm e}^{2}-288 x^{3} {\mathrm e}+144 x^{4}\right ) \ln \left (5\right )^{2}+\left (-6 \,{\mathrm e}^{2} x +24 x^{2} {\mathrm e}-24 x^{3}\right ) \ln \left (5\right )+x^{2}}\) | \(69\) |
norman | \({\mathrm e}^{\left (9 \,{\mathrm e}^{4}-72 x \,{\mathrm e}^{3}+216 x^{2} {\mathrm e}^{2}-288 x^{3} {\mathrm e}+144 x^{4}\right ) \ln \left (5\right )^{2}+\left (-6 \,{\mathrm e}^{2} x +24 x^{2} {\mathrm e}-24 x^{3}\right ) \ln \left (5\right )+x^{2}}\) | \(69\) |
risch | \(15625^{-\left ({\mathrm e}^{2}-4 x \,{\mathrm e}+4 x^{2}\right ) x} {\mathrm e}^{-288 \,{\mathrm e} \ln \left (5\right )^{2} x^{3}+144 x^{4} \ln \left (5\right )^{2}+216 \ln \left (5\right )^{2} {\mathrm e}^{2} x^{2}-72 \ln \left (5\right )^{2} {\mathrm e}^{3} x +9 \ln \left (5\right )^{2} {\mathrm e}^{4}+x^{2}}\) | \(73\) |
gosper | \({\mathrm e}^{9 \ln \left (5\right )^{2} {\mathrm e}^{4}-72 \ln \left (5\right )^{2} {\mathrm e}^{3} x +216 \ln \left (5\right )^{2} {\mathrm e}^{2} x^{2}-288 \,{\mathrm e} \ln \left (5\right )^{2} x^{3}+144 x^{4} \ln \left (5\right )^{2}-6 x \,{\mathrm e}^{2} \ln \left (5\right )+24 x^{2} {\mathrm e} \ln \left (5\right )-24 x^{3} \ln \left (5\right )+x^{2}}\) | \(85\) |
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. 76 vs.
\(2 (21) = 42\).
time = 0.65, size = 76, normalized size = 3.62 \begin {gather*} e^{\left (144 \, x^{4} \log \left (5\right )^{2} - 288 \, x^{3} e \log \left (5\right )^{2} + 216 \, x^{2} e^{2} \log \left (5\right )^{2} - 24 \, x^{3} \log \left (5\right ) + 24 \, x^{2} e \log \left (5\right ) - 72 \, x e^{3} \log \left (5\right )^{2} - 6 \, x e^{2} \log \left (5\right ) + 9 \, e^{4} \log \left (5\right )^{2} + 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. 59 vs.
\(2 (21) = 42\).
time = 0.45, size = 59, normalized size = 2.81 \begin {gather*} e^{\left (9 \, {\left (16 \, x^{4} - 32 \, x^{3} e + 24 \, x^{2} e^{2} - 8 \, x e^{3} + e^{4}\right )} \log \left (5\right )^{2} + x^{2} - 6 \, {\left (4 \, x^{3} - 4 \, x^{2} e + x e^{2}\right )} \log \left (5\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. 66 vs.
\(2 (17) = 34\).
time = 0.11, size = 66, normalized size = 3.14 \begin {gather*} e^{x^{2} + \left (- 24 x^{3} + 24 e x^{2} - 6 x e^{2}\right ) \log {\left (5 \right )} + \left (144 x^{4} - 288 e x^{3} + 216 x^{2} e^{2} - 72 x e^{3} + 9 e^{4}\right ) \log {\left (5 \right )}^{2}} \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. 76 vs.
\(2 (21) = 42\).
time = 0.55, size = 76, normalized size = 3.62 \begin {gather*} e^{\left (144 \, x^{4} \log \left (5\right )^{2} - 288 \, x^{3} e \log \left (5\right )^{2} + 216 \, x^{2} e^{2} \log \left (5\right )^{2} - 24 \, x^{3} \log \left (5\right ) + 24 \, x^{2} e \log \left (5\right ) - 72 \, x e^{3} \log \left (5\right )^{2} - 6 \, x e^{2} \log \left (5\right ) + 9 \, e^{4} \log \left (5\right )^{2} + x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.49, size = 85, normalized size = 4.05 \begin {gather*} \frac {5^{24\,x^2\,\mathrm {e}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{144\,x^4\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{-72\,x\,{\mathrm {e}}^3\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{216\,x^2\,{\mathrm {e}}^2\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{-288\,x^3\,\mathrm {e}\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{9\,{\mathrm {e}}^4\,{\ln \left (5\right )}^2}}{5^{24\,x^3}\,5^{6\,x\,{\mathrm {e}}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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