Integrand size = 23, antiderivative size = 22 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=x \left (x+4 \left (2-2 x-\left (e^e+2 x\right )^2\right )\right ) \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6} \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=-16 x^3-\left (7+16 e^e\right ) x^2+4 \left (2-e^{2 e}\right ) x \]
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Rule 6
Rubi steps \begin{align*} \text {integral}& = \int \left (8-4 e^{2 e}+\left (-14-32 e^e\right ) x-48 x^2\right ) \, dx \\ & = 4 \left (2-e^{2 e}\right ) x-\left (7+16 e^e\right ) x^2-16 x^3 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=8 x-4 e^{2 e} x-7 x^2-16 e^e x^2-16 x^3 \]
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Time = 0.04 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23
method | result | size |
gosper | \(-x \left (4 \,{\mathrm e}^{2 \,{\mathrm e}}+16 x \,{\mathrm e}^{{\mathrm e}}+16 x^{2}+7 x -8\right )\) | \(27\) |
norman | \(\left (-4 \,{\mathrm e}^{2 \,{\mathrm e}}+8\right ) x +\left (-16 \,{\mathrm e}^{{\mathrm e}}-7\right ) x^{2}-16 x^{3}\) | \(29\) |
default | \(-4 \,{\mathrm e}^{2 \,{\mathrm e}} x -16 x^{2} {\mathrm e}^{{\mathrm e}}-16 x^{3}-7 x^{2}+8 x\) | \(31\) |
risch | \(-4 \,{\mathrm e}^{2 \,{\mathrm e}} x -16 x^{2} {\mathrm e}^{{\mathrm e}}-16 x^{3}-7 x^{2}+8 x\) | \(31\) |
parallelrisch | \(-16 x^{2} {\mathrm e}^{{\mathrm e}}-16 x^{3}-7 x^{2}+\left (-4 \,{\mathrm e}^{2 \,{\mathrm e}}+8\right ) x\) | \(31\) |
parts | \(-4 \,{\mathrm e}^{2 \,{\mathrm e}} x -16 x^{2} {\mathrm e}^{{\mathrm e}}-16 x^{3}-7 x^{2}+8 x\) | \(31\) |
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Time = 0.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=-16 \, x^{3} - 16 \, x^{2} e^{e} - 7 \, x^{2} - 4 \, x e^{\left (2 \, e\right )} + 8 \, x \]
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Time = 0.02 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.32 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=- 16 x^{3} + x^{2} \left (- 16 e^{e} - 7\right ) + x \left (8 - 4 e^{2 e}\right ) \]
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Time = 0.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=-16 \, x^{3} - 16 \, x^{2} e^{e} - 7 \, x^{2} - 4 \, x e^{\left (2 \, e\right )} + 8 \, x \]
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Time = 0.28 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=-16 \, x^{3} - 16 \, x^{2} e^{e} - 7 \, x^{2} - 4 \, x e^{\left (2 \, e\right )} + 8 \, x \]
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Time = 0.04 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (8-4 e^{2 e}-14 x-32 e^e x-48 x^2\right ) \, dx=-16\,x^3+\left (-16\,{\mathrm {e}}^{\mathrm {e}}-7\right )\,x^2+\left (8-4\,{\mathrm {e}}^{2\,\mathrm {e}}\right )\,x \]
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