Integrand size = 44, antiderivative size = 20 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=x^4 \left (-1+2 x+e^{21-e^x} x\right ) \]
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\[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=\int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (5 e^{21-e^x} x^4-e^{21-e^x+x} x^5+2 x^3 (-2+5 x)\right ) \, dx \\ & = 2 \int x^3 (-2+5 x) \, dx+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx \\ & = 2 \int \left (-2 x^3+5 x^4\right ) \, dx+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx \\ & = -x^4+2 x^5+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx \\ \end{align*}
Time = 0.12 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=x^4 \left (-1+\left (2+e^{21-e^x}\right ) x\right ) \]
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Time = 0.34 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15
method | result | size |
risch | \(2 x^{5}-x^{4}+x^{5} {\mathrm e}^{21-{\mathrm e}^{x}}\) | \(23\) |
norman | \(\left (x^{5} {\mathrm e}^{21}-x^{4} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\right ) {\mathrm e}^{-{\mathrm e}^{x}}\) | \(30\) |
parallelrisch | \(\left (x^{5} {\mathrm e}^{21}-x^{4} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\right ) {\mathrm e}^{-{\mathrm e}^{x}}\) | \(30\) |
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Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.40 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx={\left (x^{5} e^{21} + {\left (2 \, x^{5} - x^{4}\right )} e^{\left (e^{x}\right )}\right )} e^{\left (-e^{x}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=2 x^{5} + x^{5} e^{21} e^{- e^{x}} - x^{4} \]
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=x^{5} e^{\left (-e^{x} + 21\right )} + 2 \, x^{5} - x^{4} \]
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Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=x^{5} e^{\left (-e^{x} + 21\right )} + 2 \, x^{5} - x^{4} \]
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Time = 12.39 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx=2\,x^5-x^4+x^5\,{\mathrm {e}}^{21}\,{\mathrm {e}}^{-{\mathrm {e}}^x} \]
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