Integrand size = 52, antiderivative size = 25 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=e^{e^{-1-e^x+2 x}+x-(5+x)^2}+x \]
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Time = 0.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6838} \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=e^{-x^2-9 x+e^{2 x-e^x-1}-25}+x \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = x+\int e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right ) \, dx \\ & = e^{-25+e^{-1-e^x+2 x}-9 x-x^2}+x \\ \end{align*}
Time = 1.68 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=e^{-25+e^{-1-e^x+2 x}-9 x-x^2}+x \]
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Time = 0.14 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96
method | result | size |
default | \(x +{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+2 x -1}-x^{2}-9 x -25}\) | \(24\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+2 x -1}-x^{2}-9 x -25}\) | \(24\) |
risch | \(x +{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+2 x -1}-x^{2}-9 x -25}\) | \(24\) |
parallelrisch | \(x +{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+2 x -1}-x^{2}-9 x -25}\) | \(24\) |
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none
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=x + e^{\left (-x^{2} - 9 \, x + e^{\left (2 \, x - e^{x} - 1\right )} - 25\right )} \]
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Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=x + e^{- x^{2} - 9 x + e^{2 x - e^{x} - 1} - 25} \]
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none
Time = 0.47 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=x + e^{\left (-x^{2} - 9 \, x + e^{\left (2 \, x - e^{x} - 1\right )} - 25\right )} \]
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none
Time = 0.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=x + e^{\left (-x^{2} - 9 \, x + e^{\left (2 \, x - e^{x} - 1\right )} - 25\right )} \]
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Time = 0.19 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \left (1+e^{-25+e^{-1-e^x+2 x}-9 x-x^2} \left (-9+e^{-1-e^x+2 x} \left (2-e^x\right )-2 x\right )\right ) \, dx=x+{\mathrm {e}}^{{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-9\,x}\,{\mathrm {e}}^{-25}\,{\mathrm {e}}^{-x^2} \]
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