Optimal. Leaf size=24 \[ e^{x \left (4+\log (5)-x \left (5+x+\frac {\log (3-x)}{x}\right )\right )} \]
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Rubi [A]
time = 0.35, antiderivative size = 29, normalized size of antiderivative = 1.21, number of steps
used = 1, number of rules used = 1, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6838}
\begin {gather*} 5^x e^{-x^3-5 x^2+4 x} (3-x)^{-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5^x e^{4 x-5 x^2-x^3} (3-x)^{-x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 1.31, size = 26, normalized size = 1.08 \begin {gather*} 5^x e^{-x \left (-4+5 x+x^2\right )} (3-x)^{-x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 26, normalized size = 1.08
method | result | size |
risch | \(\left (3-x \right )^{-x} 5^{x} {\mathrm e}^{-x \left (x^{2}+5 x -4\right )}\) | \(26\) |
norman | \({\mathrm e}^{-x \ln \left (3-x \right )+x \ln \left (5\right )-x^{3}-5 x^{2}+4 x}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (-x^{3} - 5 \, x^{2} + x \log \left (5\right ) - x \log \left (-x + 3\right ) + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (-x^{3} - 5 \, x^{2} + x \log \left (5\right ) - x \log \left (-x + 3\right ) + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 24, normalized size = 1.00 \begin {gather*} e^{- x^{3} - 5 x^{2} - x \log {\left (3 - x \right )} + x \log {\left (5 \right )} + 4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 28, normalized size = 1.17 \begin {gather*} e^{\left (-x^{3} - 5 \, x^{2} + x \log \left (5\right ) - x \log \left (-x + 3\right ) + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.48, size = 29, normalized size = 1.21 \begin {gather*} \frac {5^x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{-5\,x^2}}{{\left (3-x\right )}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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