Integrand size = 72, antiderivative size = 31 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=-4+x^2 \left (e^{3 \left (-x+x^2 \left (-x+e^{-x} x\right )\right )}+x\right ) \]
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\[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=\int e^{-x} \left (3 e^x x^2+\exp \left (e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )\right ) \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x \left (3 x-e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} \left (3 (-3+x) x^3+e^x \left (-2+3 x+9 x^3\right )\right )\right ) \, dx \\ & = \int \left (3 x^2-e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x \left (-2 e^x+3 e^x x-9 x^3+9 e^x x^3+3 x^4\right )\right ) \, dx \\ & = x^3-\int e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x \left (-2 e^x+3 e^x x-9 x^3+9 e^x x^3+3 x^4\right ) \, dx \\ & = x^3-\int \left (3 e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} (-3+x) x^4+e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x \left (-2+3 x+9 x^3\right )\right ) \, dx \\ & = x^3-3 \int e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} (-3+x) x^4 \, dx-\int e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x \left (-2+3 x+9 x^3\right ) \, dx \\ & = x^3-3 \int \left (-3 e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x^4+e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x^5\right ) \, dx-\int \left (-2 e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x+3 e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x^2+9 e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x^4\right ) \, dx \\ & = x^3+2 \int e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x \, dx-3 \int e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x^2 \, dx-3 \int e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x^5 \, dx+9 \int e^{-4 x+\left (-3+3 e^{-x}\right ) x^3} x^4 \, dx-9 \int e^{-3 x+\left (-3+3 e^{-x}\right ) x^3} x^4 \, dx \\ \end{align*}
Time = 5.15 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.81 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=x^2 \left (e^{-3 x+\left (-3+3 e^{-x}\right ) x^3}+x\right ) \]
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Time = 0.22 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00
method | result | size |
risch | \(x^{3}+x^{2} {\mathrm e}^{-3 x \left ({\mathrm e}^{x} x^{2}-x^{2}+{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}\) | \(31\) |
parallelrisch | \(x^{3}+x^{2} {\mathrm e}^{\left (\left (-3 x^{3}-3 x \right ) {\mathrm e}^{x}+3 x^{3}\right ) {\mathrm e}^{-x}}\) | \(33\) |
norman | \(\left ({\mathrm e}^{x} x^{3}+{\mathrm e}^{x} x^{2} {\mathrm e}^{\left (\left (-3 x^{3}-3 x \right ) {\mathrm e}^{x}+3 x^{3}\right ) {\mathrm e}^{-x}}\right ) {\mathrm e}^{-x}\) | \(43\) |
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Time = 0.27 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.90 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=x^{3} + x^{2} e^{\left (3 \, {\left (x^{3} - {\left (x^{3} + x\right )} e^{x}\right )} e^{\left (-x\right )}\right )} \]
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Time = 0.17 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=x^{3} + x^{2} e^{\left (3 x^{3} + \left (- 3 x^{3} - 3 x\right ) e^{x}\right ) e^{- x}} \]
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Time = 0.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=x^{3} + x^{2} e^{\left (3 \, x^{3} e^{\left (-x\right )} - 3 \, x^{3} - 3 \, x\right )} \]
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\[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=\int { {\left (3 \, x^{2} e^{x} - {\left (3 \, x^{5} - 9 \, x^{4} + {\left (9 \, x^{4} + 3 \, x^{2} - 2 \, x\right )} e^{x}\right )} e^{\left (3 \, {\left (x^{3} - {\left (x^{3} + x\right )} e^{x}\right )} e^{\left (-x\right )}\right )}\right )} e^{\left (-x\right )} \,d x } \]
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Time = 17.37 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.90 \[ \int e^{-x} \left (3 e^x x^2+e^{e^{-x} \left (3 x^3+e^x \left (-3 x-3 x^3\right )\right )} \left (9 x^4-3 x^5+e^x \left (2 x-3 x^2-9 x^4\right )\right )\right ) \, dx=x^3+x^2\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-3\,x^3}\,{\mathrm {e}}^{3\,x^3\,{\mathrm {e}}^{-x}} \]
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