Optimal. Leaf size=15 \[ e^{-e^{\frac {1}{5+x}}} (-3+x) \]
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Rubi [A]
time = 0.06, antiderivative size = 18, normalized size of antiderivative = 1.20, number of steps
used = 2, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {27, 2326}
\begin {gather*} -e^{-e^{\frac {1}{x+5}}} (3-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-e^{\frac {1}{5+x}}} \left (25+e^{\frac {1}{5+x}} (-3+x)+10 x+x^2\right )}{(5+x)^2} \, dx\\ &=-e^{-e^{\frac {1}{5+x}}} (3-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} e^{-e^{\frac {1}{5+x}}} (-3+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 4.11, size = 14, normalized size = 0.93
method | result | size |
risch | \(\left (x -3\right ) {\mathrm e}^{-{\mathrm e}^{\frac {1}{5+x}}}\) | \(14\) |
norman | \(\frac {\left (x^{2}+2 x -15\right ) {\mathrm e}^{-{\mathrm e}^{\frac {1}{5+x}}}}{5+x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.87 \begin {gather*} {\left (x - 3\right )} e^{\left (-e^{\left (\frac {1}{x + 5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 13, normalized size = 0.87 \begin {gather*} {\left (x - 3\right )} e^{\left (-e^{\left (\frac {1}{x + 5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.68, size = 10, normalized size = 0.67 \begin {gather*} \left (x - 3\right ) e^{- e^{\frac {1}{x + 5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 1.53 \begin {gather*} x e^{\left (-e^{\left (\frac {1}{x + 5}\right )}\right )} - 3 \, e^{\left (-e^{\left (\frac {1}{x + 5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 13, normalized size = 0.87 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^{\frac {1}{x+5}}}\,\left (x-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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