Integrand size = 29, antiderivative size = 11 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{e^{-x}+e^x} \]
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\[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=\int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -\int e^{e^{-x}+e^x-x} \, dx+\int e^{e^{-x}+e^x+x} \, dx \\ & = \text {Subst}\left (\int e^{\frac {1}{x}+x} \, dx,x,e^x\right )-\text {Subst}\left (\int \frac {e^{\frac {1}{x}+x}}{x^2} \, dx,x,e^x\right ) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{e^{-x}+e^x} \]
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Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{-x}}\) | \(9\) |
norman | \({\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{-x}-x} {\mathrm e}^{x}\) | \(15\) |
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Leaf count of result is larger than twice the leaf count of optimal. 20 vs. \(2 (8) = 16\).
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.82 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{\left ({\left (x e^{x} + e^{\left (2 \, x\right )} + 1\right )} e^{\left (-x\right )} - x\right )} \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.27 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{x} e^{- x + e^{x} + e^{- x}} \]
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none
Time = 0.28 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{\left (e^{\left (-x\right )} + e^{x}\right )} \]
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none
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx=e^{\left ({\left (e^{\left (2 \, x\right )} + 1\right )} e^{\left (-x\right )}\right )} \]
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Time = 14.76 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (-e^{e^{-x}+e^x-x}+e^{e^{-x}+e^x+x}\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{-x}+{\mathrm {e}}^x} \]
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