Optimal. Leaf size=17 \[ 5+x+e^{-4+e^{e^e}-x} x \]
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Rubi [A]
time = 0.08, antiderivative size = 33, normalized size of antiderivative = 1.94, number of steps
used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6820, 2207,
2225} \begin {gather*} -e^{-x+e^{e^e}-4} (1-x)+e^{-x+e^{e^e}-4}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-e^{-4+e^{e^e}-x} (-1+x)\right ) \, dx\\ &=x-\int e^{-4+e^{e^e}-x} (-1+x) \, dx\\ &=-e^{-4+e^{e^e}-x} (1-x)+x-\int e^{-4+e^{e^e}-x} \, dx\\ &=e^{-4+e^{e^e}-x}-e^{-4+e^{e^e}-x} (1-x)+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 16, normalized size = 0.94 \begin {gather*} x+e^{-4+e^{e^e}-x} x \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. \(50\) vs.
\(2(19)=38\).
time = 0.08, size = 51, normalized size = 3.00
method | result | size |
risch | \(x +x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x}\) | \(15\) |
norman | \(\left (1+x \,{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-\ln \left (x \right )+4+x}\right ) x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x}\) | \(36\) |
default | \(x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x} \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x \right )-4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}}}-4-x}\) | \(51\) |
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. 34 vs.
\(2 (15) = 30\).
time = 0.26, size = 34, normalized size = 2.00 \begin {gather*} {\left (x e^{\left (e^{\left (e^{e}\right )}\right )} + e^{\left (e^{\left (e^{e}\right )}\right )}\right )} e^{\left (-x - 4\right )} + x - e^{\left (-x + e^{\left (e^{e}\right )} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 14, normalized size = 0.82 \begin {gather*} x + e^{\left (-x + e^{\left (e^{e}\right )} + \log \left (x\right ) - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.82 \begin {gather*} x e^{- x - 4 + e^{e^{e}}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 14, normalized size = 0.82 \begin {gather*} x e^{\left (-x + e^{\left (e^{e}\right )} - 4\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.38, size = 16, normalized size = 0.94 \begin {gather*} x\,\left ({\mathrm {e}}^{-x}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\mathrm {e}}}}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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