Optimal. Leaf size=27 \[ e^{x+e^4 \left (x-x^2 \left (4+\frac {x^2}{6+\log (5)}\right )\right )} \]
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Rubi [A]
time = 0.26, antiderivative size = 54, normalized size of antiderivative = 2.00, number of steps
used = 2, number of rules used = 2, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {12, 6838}
\begin {gather*} 5^{\frac {e^4 \left (x-4 x^2\right )+x}{6+\log (5)}} \exp \left (\frac {e^4 \left (-x^4-24 x^2+6 x\right )+6 x}{6+\log (5)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \exp \left (\frac {6 x+e^4 \left (6 x-24 x^2-x^4\right )+\left (x+e^4 \left (x-4 x^2\right )\right ) \log (5)}{6+\log (5)}\right ) \left (6+e^4 \left (6-48 x-4 x^3\right )+\left (1+e^4 (1-8 x)\right ) \log (5)\right ) \, dx}{6+\log (5)}\\ &=5^{\frac {x+e^4 \left (x-4 x^2\right )}{6+\log (5)}} e^{\frac {6 x+e^4 \left (6 x-24 x^2-x^4\right )}{6+\log (5)}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.85, size = 47, normalized size = 1.74 \begin {gather*} 5^{\frac {x+e^4 (1-4 x) x}{6+\log (5)}} e^{\frac {x \left (6-e^4 \left (-6+24 x+x^3\right )\right )}{6+\log (5)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 1.67
method | result | size |
gosper | \({\mathrm e}^{-\frac {x \left (x^{3} {\mathrm e}^{4}+4 x \,{\mathrm e}^{4} \ln \left (5\right )-{\mathrm e}^{4} \ln \left (5\right )+24 x \,{\mathrm e}^{4}-\ln \left (5\right )-6 \,{\mathrm e}^{4}-6\right )}{\ln \left (5\right )+6}}\) | \(45\) |
derivativedivides | \({\mathrm e}^{\frac {\left (\left (-4 x^{2}+x \right ) {\mathrm e}^{4}+x \right ) \ln \left (5\right )+\left (-x^{4}-24 x^{2}+6 x \right ) {\mathrm e}^{4}+6 x}{\ln \left (5\right )+6}}\) | \(45\) |
default | \({\mathrm e}^{\frac {\left (\left (-4 x^{2}+x \right ) {\mathrm e}^{4}+x \right ) \ln \left (5\right )+\left (-x^{4}-24 x^{2}+6 x \right ) {\mathrm e}^{4}+6 x}{\ln \left (5\right )+6}}\) | \(45\) |
norman | \({\mathrm e}^{\frac {\left (\left (-4 x^{2}+x \right ) {\mathrm e}^{4}+x \right ) \ln \left (5\right )+\left (-x^{4}-24 x^{2}+6 x \right ) {\mathrm e}^{4}+6 x}{\ln \left (5\right )+6}}\) | \(45\) |
risch | \({\mathrm e}^{-\frac {x \left (x^{3} {\mathrm e}^{4}+4 x \,{\mathrm e}^{4} \ln \left (5\right )-{\mathrm e}^{4} \ln \left (5\right )+24 x \,{\mathrm e}^{4}-\ln \left (5\right )-6 \,{\mathrm e}^{4}-6\right )}{\ln \left (5\right )+6}}\) | \(45\) |
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. 85 vs.
\(2 (27) = 54\).
time = 0.60, size = 85, normalized size = 3.15 \begin {gather*} e^{\left (-\frac {x^{4} e^{4}}{\log \left (5\right ) + 6} - \frac {4 \, x^{2} e^{4} \log \left (5\right )}{\log \left (5\right ) + 6} - \frac {24 \, x^{2} e^{4}}{\log \left (5\right ) + 6} + \frac {x e^{4} \log \left (5\right )}{\log \left (5\right ) + 6} + \frac {6 \, x e^{4}}{\log \left (5\right ) + 6} + \frac {x \log \left (5\right )}{\log \left (5\right ) + 6} + \frac {6 \, x}{\log \left (5\right ) + 6}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 47, normalized size = 1.74 \begin {gather*} e^{\left (-\frac {{\left (x^{4} + 24 \, x^{2} - 6 \, x\right )} e^{4} + {\left ({\left (4 \, x^{2} - x\right )} e^{4} - x\right )} \log \left (5\right ) - 6 \, x}{\log \left (5\right ) + 6}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 39, normalized size = 1.44 \begin {gather*} e^{\frac {6 x + \left (x + \left (- 4 x^{2} + x\right ) e^{4}\right ) \log {\left (5 \right )} + \left (- x^{4} - 24 x^{2} + 6 x\right ) e^{4}}{\log {\left (5 \right )} + 6}} \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. 117 vs.
\(2 (27) = 54\).
time = 0.53, size = 117, normalized size = 4.33 \begin {gather*} \frac {e^{\left (-\frac {x^{4} e^{4} + 4 \, x^{2} e^{4} \log \left (5\right ) + 24 \, x^{2} e^{4} - x e^{4} \log \left (5\right ) - 6 \, x e^{4} - x \log \left (5\right ) - 6 \, x}{\log \left (5\right ) + 6}\right )} \log \left (5\right ) + 6 \, e^{\left (-\frac {x^{4} e^{4} + 4 \, x^{2} e^{4} \log \left (5\right ) + 24 \, x^{2} e^{4} - x e^{4} \log \left (5\right ) - 6 \, x e^{4} - x \log \left (5\right ) - 6 \, x}{\log \left (5\right ) + 6}\right )}}{\log \left (5\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.42, size = 73, normalized size = 2.70 \begin {gather*} 5^{\frac {x+x\,{\mathrm {e}}^4-4\,x^2\,{\mathrm {e}}^4}{\ln \left (5\right )+6}}\,{\mathrm {e}}^{-\frac {x^4\,{\mathrm {e}}^4}{\ln \left (5\right )+6}}\,{\mathrm {e}}^{-\frac {24\,x^2\,{\mathrm {e}}^4}{\ln \left (5\right )+6}}\,{\mathrm {e}}^{\frac {6\,x}{\ln \left (5\right )+6}}\,{\mathrm {e}}^{\frac {6\,x\,{\mathrm {e}}^4}{\ln \left (5\right )+6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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