Integrand size = 152, antiderivative size = 35 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\frac {5}{3 x \left (-e^5+\frac {e^{3/x}-2 x}{16-x}+x\right )} \]
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\[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {5 \left (e^5 (-16+x)^2 x-e^{3/x} (-48+19 x)-2 x^2 \left (224-31 x+x^2\right )\right )}{3 x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx \\ & = \frac {5}{3} \int \frac {e^5 (-16+x)^2 x-e^{3/x} (-48+19 x)-2 x^2 \left (224-31 x+x^2\right )}{x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx \\ & = \frac {5}{3} \int \left (\frac {-48+19 x}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )}+\frac {(16-x) \left (48 e^5-3 \left (14+e^5\right ) x-\left (11+e^5\right ) x^2+2 x^3\right )}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}\right ) \, dx \\ & = \frac {5}{3} \int \frac {-48+19 x}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )} \, dx+\frac {5}{3} \int \frac {(16-x) \left (48 e^5-3 \left (14+e^5\right ) x-\left (11+e^5\right ) x^2+2 x^3\right )}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx \\ & = \frac {5}{3} \int \frac {(16-x) \left (48 e^5-3 \left (14+e^5\right ) x-\left (11+e^5\right ) x^2+2 x^3\right )}{x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx+\frac {5}{3} \int \left (\frac {48}{x^3 \left (-16 e^5+e^{3/x}+14 \left (1+\frac {e^5}{14}\right ) x-x^2\right )}+\frac {19}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )}\right ) \, dx \\ & = \frac {5}{3} \int \left (\frac {43 \left (1+\frac {e^5}{43}\right )}{\left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}+\frac {768 e^5}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}+\frac {96 \left (-7-e^5\right )}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}+\frac {-134-13 e^5}{x \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}-\frac {2 x}{\left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2}\right ) \, dx+\frac {95}{3} \int \frac {1}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )} \, dx+80 \int \frac {1}{x^3 \left (-16 e^5+e^{3/x}+14 \left (1+\frac {e^5}{14}\right ) x-x^2\right )} \, dx \\ & = -\left (\frac {10}{3} \int \frac {x}{\left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx\right )+\frac {95}{3} \int \frac {1}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )} \, dx+80 \int \frac {1}{x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )} \, dx+\left (1280 e^5\right ) \int \frac {1}{x^3 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx-\left (160 \left (7+e^5\right )\right ) \int \frac {1}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx+\frac {1}{3} \left (5 \left (43+e^5\right )\right ) \int \frac {1}{\left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx-\frac {1}{3} \left (5 \left (134+13 e^5\right )\right ) \int \frac {1}{x \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )^2} \, dx \\ & = -\left (\frac {10}{3} \int \frac {x}{\left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx\right )+\frac {95}{3} \int \frac {1}{x^2 \left (16 e^5-e^{3/x}-14 \left (1+\frac {e^5}{14}\right ) x+x^2\right )} \, dx+80 \int \frac {1}{x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )} \, dx+\left (1280 e^5\right ) \int \frac {1}{x^3 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx-\left (160 \left (7+e^5\right )\right ) \int \frac {1}{x^2 \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx+\frac {1}{3} \left (5 \left (43+e^5\right )\right ) \int \frac {1}{\left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx-\frac {1}{3} \left (5 \left (134+13 e^5\right )\right ) \int \frac {1}{x \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )^2} \, dx \\ \end{align*}
Time = 0.82 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.94 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=-\frac {5 (-16+x)}{3 x \left (e^{3/x}+e^5 (-16+x)-(-14+x) x\right )} \]
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Time = 5.50 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.97
method | result | size |
risch | \(-\frac {5 \left (x -16\right )}{3 x \left (x \,{\mathrm e}^{5}-x^{2}-16 \,{\mathrm e}^{5}+{\mathrm e}^{\frac {3}{x}}+14 x \right )}\) | \(34\) |
parallelrisch | \(\frac {80-5 x}{3 x \left (x \,{\mathrm e}^{5}-x^{2}-16 \,{\mathrm e}^{5}+{\mathrm e}^{\frac {3}{x}}+14 x \right )}\) | \(36\) |
norman | \(\frac {-\frac {5}{3} x^{2}+\frac {80}{3} x}{x^{2} \left (x \,{\mathrm e}^{5}-x^{2}-16 \,{\mathrm e}^{5}+{\mathrm e}^{\frac {3}{x}}+14 x \right )}\) | \(39\) |
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Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.03 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\frac {5 \, {\left (x - 16\right )}}{3 \, {\left (x^{3} - 14 \, x^{2} - {\left (x^{2} - 16 \, x\right )} e^{5} - x e^{\frac {3}{x}}\right )}} \]
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Time = 0.10 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\frac {80 - 5 x}{- 3 x^{3} + 42 x^{2} + 3 x^{2} e^{5} + 3 x e^{\frac {3}{x}} - 48 x e^{5}} \]
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Time = 0.24 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.97 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\frac {5 \, {\left (x - 16\right )}}{3 \, {\left (x^{3} - x^{2} {\left (e^{5} + 14\right )} + 16 \, x e^{5} - x e^{\frac {3}{x}}\right )}} \]
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Time = 0.49 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.23 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=-\frac {5 \, {\left (\frac {1}{x^{2}} - \frac {16}{x^{3}}\right )}}{3 \, {\left (\frac {e^{5}}{x} + \frac {14}{x} - \frac {16 \, e^{5}}{x^{2}} + \frac {e^{\frac {3}{x}}}{x^{2}} - 1\right )}} \]
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Time = 9.91 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.03 \[ \int \frac {e^{3/x} (240-95 x)-2240 x^2+310 x^3-10 x^4+e^5 \left (1280 x-160 x^2+5 x^3\right )}{3 e^{6/x} x^3+588 x^5-84 x^6+3 x^7+e^{10} \left (768 x^3-96 x^4+3 x^5\right )+e^5 \left (-1344 x^4+180 x^5-6 x^6\right )+e^{3/x} \left (84 x^4-6 x^5+e^5 \left (-96 x^3+6 x^4\right )\right )} \, dx=\frac {\frac {10\,x^5}{3}+\left (-\frac {5\,{\mathrm {e}}^5}{3}-\frac {215}{3}\right )\,x^4+\left (\frac {65\,{\mathrm {e}}^5}{3}+\frac {670}{3}\right )\,x^3+\left (160\,{\mathrm {e}}^5+1120\right )\,x^2-1280\,{\mathrm {e}}^5\,x}{\left (14\,x-16\,{\mathrm {e}}^5+{\mathrm {e}}^{3/x}+x\,{\mathrm {e}}^5-x^2\right )\,\left (3\,x^3\,{\mathrm {e}}^5-48\,x^2\,{\mathrm {e}}^5+x^4\,{\mathrm {e}}^5+42\,x^3+11\,x^4-2\,x^5\right )} \]
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