Optimal. Leaf size=26 \[ -e^{e^{1+e^{\frac {e x^2}{5}}}-x}+2 x \]
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Rubi [A] time = 0.16, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {12, 6706} \begin {gather*} 2 x-e^{e^{e^{\frac {e x^2}{5}}+1}-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (10+e^{e^{1+e^{\frac {e x^2}{5}}}-x} \left (5-2 e^{2+e^{\frac {e x^2}{5}}+\frac {e x^2}{5}} x\right )\right ) \, dx\\ &=2 x+\frac {1}{5} \int e^{e^{1+e^{\frac {e x^2}{5}}}-x} \left (5-2 e^{2+e^{\frac {e x^2}{5}}+\frac {e x^2}{5}} x\right ) \, dx\\ &=-e^{e^{1+e^{\frac {e x^2}{5}}}-x}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 26, normalized size = 1.00 \begin {gather*} -e^{e^{1+e^{\frac {e x^2}{5}}}-x}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 52, normalized size = 2.00 \begin {gather*} 2 \, x - e^{\left (-{\left (x e^{\left (\frac {1}{5} \, x^{2} e + 1\right )} - e^{\left (\frac {1}{5} \, x^{2} e + e^{\left (\frac {1}{5} \, x^{2} e\right )} + 2\right )}\right )} e^{\left (-\frac {1}{5} \, x^{2} e - 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 22, normalized size = 0.85 \begin {gather*} 2 \, x - e^{\left (-x + e^{\left (e^{\left (\frac {1}{5} \, x^{2} e\right )} + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 23, normalized size = 0.88
method | result | size |
default | \(2 x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{2} {\mathrm e}}{5}}+1}-x}\) | \(23\) |
norman | \(2 x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{2} {\mathrm e}}{5}}+1}-x}\) | \(23\) |
risch | \(2 x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{2} {\mathrm e}}{5}}+1}-x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 22, normalized size = 0.85 \begin {gather*} 2 \, x - e^{\left (-x + e^{\left (e^{\left (\frac {1}{5} \, x^{2} e\right )} + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 24, normalized size = 0.92 \begin {gather*} 2\,x-{\mathrm {e}}^{-x}\,{\mathrm {e}}^{\mathrm {e}\,{\mathrm {e}}^{{\left ({\mathrm {e}}^{x^2\,\mathrm {e}}\right )}^{1/5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 19, normalized size = 0.73 \begin {gather*} 2 x - e^{- x + e^{e^{\frac {e x^{2}}{5}} + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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