Integrand size = 66, antiderivative size = 28 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=e^{2 e^{e^{5+x^2}-x} x}+\left (-2+e^x\right ) x^3 \]
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\[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=\int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = -2 x^3+\int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right ) \, dx+\int e^x \left (3 x^2+x^3\right ) \, dx \\ & = -2 x^3+\int e^x x^2 (3+x) \, dx+\int 2 e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (1-x+2 e^{5+x^2} x^2\right ) \, dx \\ & = -2 x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (1-x+2 e^{5+x^2} x^2\right ) \, dx+\int \left (3 e^x x^2+e^x x^3\right ) \, dx \\ & = -2 x^3+2 \int \left (e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x}-e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x+2 e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2\right ) \, dx+3 \int e^x x^2 \, dx+\int e^x x^3 \, dx \\ & = 3 e^x x^2-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx-3 \int e^x x^2 \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx-6 \int e^x x \, dx \\ & = -6 e^x x-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx+6 \int e^x \, dx+6 \int e^x x \, dx \\ & = 6 e^x-2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx-6 \int e^x \, dx \\ & = -2 x^3+e^x x^3+2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \, dx-2 \int e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} x \, dx+4 \int e^{5+e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x+x^2} x^2 \, dx \\ \end{align*}
Time = 1.10 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=e^{2 e^{e^{5+x^2}-x} x}-2 x^3+e^x x^3 \]
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Time = 3.15 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
method | result | size |
risch | \({\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{x^{2}+5}-x}}-2 x^{3}\) | \(28\) |
default | \({\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{5} {\mathrm e}^{x^{2}}-x}}-2 x^{3}\) | \(29\) |
parallelrisch | \({\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x \,{\mathrm e}^{{\mathrm e}^{5} {\mathrm e}^{x^{2}}-x}}-2 x^{3}\) | \(29\) |
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Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (24) = 48\).
Time = 0.25 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.21 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx={\left ({\left (x^{3} e^{x} - 2 \, x^{3}\right )} e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} + e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} - x + e^{\left (x^{2} + 5\right )}\right )}\right )} e^{\left (x - e^{\left (x^{2} + 5\right )}\right )} \]
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Time = 0.61 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=x^{3} e^{x} - 2 x^{3} + e^{2 x e^{- x + e^{5} e^{x^{2}}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (24) = 48\).
Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=-2 \, x^{3} + {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + 3 \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )}\right )} \]
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\[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx=\int { -6 \, x^{2} + 2 \, {\left (2 \, x^{2} e^{\left (x^{2} + 5\right )} - x + 1\right )} e^{\left (2 \, x e^{\left (-x + e^{\left (x^{2} + 5\right )}\right )} - x + e^{\left (x^{2} + 5\right )}\right )} + {\left (x^{3} + 3 \, x^{2}\right )} e^{x} \,d x } \]
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Time = 14.75 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \left (-6 x^2+e^{e^{5+x^2}-x+2 e^{e^{5+x^2}-x} x} \left (2-2 x+4 e^{5+x^2} x^2\right )+e^x \left (3 x^2+x^3\right )\right ) \, dx={\mathrm {e}}^{2\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^5}}+x^3\,{\mathrm {e}}^x-2\,x^3 \]
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