Integrand size = 104, antiderivative size = 33 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {1}{5} e^{\frac {x^2 \left (3-e^{x^2}+x-\log (x)\right )}{3-\frac {3}{x}}} \]
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\[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15 (-1+x)^2} \, dx \\ & = \frac {1}{15} \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{(-1+x)^2} \, dx \\ & = \frac {1}{15} \int \left (-\frac {8 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2}{(-1+x)^2}+\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^3}{(-1+x)^2}+\frac {3 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^4}{(-1+x)^2}-\frac {\exp \left (x^2+\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2 \left (-3+2 x-2 x^2+2 x^3\right )}{(-1+x)^2}-\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2 (-3+2 x) \log (x)}{(-1+x)^2}\right ) \, dx \\ & = \frac {1}{15} \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^3}{(-1+x)^2} \, dx-\frac {1}{15} \int \frac {\exp \left (x^2+\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2 \left (-3+2 x-2 x^2+2 x^3\right )}{(-1+x)^2} \, dx-\frac {1}{15} \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2 (-3+2 x) \log (x)}{(-1+x)^2} \, dx+\frac {1}{5} \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^4}{(-1+x)^2} \, dx-\frac {8}{15} \int \frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2}{(-1+x)^2} \, dx \\ & = \frac {1}{15} \int \left (2 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )+\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{(-1+x)^2}+\frac {3 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{-1+x}+\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x\right ) \, dx-\frac {1}{15} \int \frac {\exp \left (\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}\right ) x^2 \left (-3+2 x-2 x^2+2 x^3\right )}{(1-x)^2} \, dx-\frac {1}{15} \int \left (\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) \log (x)-\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) \log (x)}{(-1+x)^2}+2 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x \log (x)\right ) \, dx+\frac {1}{5} \int \left (3 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )+\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{(-1+x)^2}+\frac {4 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{-1+x}+2 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x+\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right ) x^2\right ) \, dx-\frac {8}{15} \int \left (\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )+\frac {\exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{(-1+x)^2}+\frac {2 \exp \left (\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}\right )}{-1+x}\right ) \, dx \\ & = \frac {1}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {1}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \, dx-\frac {1}{15} \int \left (3 e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}}-\frac {e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}}}{(-1+x)^2}+\frac {2 e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}}}{-1+x}+4 e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x+2 e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x^2+2 e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x^3\right ) \, dx-\frac {1}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \log (x) \, dx+\frac {1}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \log (x)}{(-1+x)^2} \, dx+\frac {2}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx-\frac {2}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \log (x) \, dx+\frac {1}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {1}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx+\frac {1}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x^2 \, dx+\frac {2}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \, dx-\frac {8}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx-\frac {8}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {3}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx+\frac {4}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx-\frac {16}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx \\ & = \frac {1}{15} \int \frac {e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}}}{(-1+x)^2} \, dx+\frac {1}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {1}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \, dx-\frac {1}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \log (x) \, dx+\frac {1}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \log (x)}{(-1+x)^2} \, dx+\frac {2}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx-\frac {2}{15} \int \frac {e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}}}{-1+x} \, dx-\frac {2}{15} \int e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x^2 \, dx-\frac {2}{15} \int e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x^3 \, dx-\frac {2}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \log (x) \, dx-\frac {1}{5} \int e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} \, dx+\frac {1}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {1}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx+\frac {1}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x^2 \, dx-\frac {4}{15} \int e^{\frac {x^2 \left (-3+6 x-e^{x^2} x+x^2-x \log (x)\right )}{3 (-1+x)}} x \, dx+\frac {2}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} x \, dx-\frac {8}{15} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx-\frac {8}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{(-1+x)^2} \, dx+\frac {3}{5} \int e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \, dx+\frac {4}{5} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx-\frac {16}{15} \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}}}{-1+x} \, dx \\ \end{align*}
Time = 0.20 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.24 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {1}{5} e^{\frac {x^3 \left (3-e^{x^2}+x\right )}{3 (-1+x)}} x^{\frac {x^3}{3-3 x}} \]
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Time = 6.65 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.76
method | result | size |
risch | \(\frac {{\mathrm e}^{-\frac {x^{3} \left (\ln \left (x \right )+{\mathrm e}^{x^{2}}-x -3\right )}{3 \left (-1+x \right )}}}{5}\) | \(25\) |
parallelrisch | \(\frac {{\mathrm e}^{-\frac {x^{3} \left (\ln \left (x \right )+{\mathrm e}^{x^{2}}-x -3\right )}{3 \left (-1+x \right )}}}{5}\) | \(25\) |
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Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {1}{5} \, e^{\left (\frac {x^{4} - x^{3} e^{\left (x^{2}\right )} - x^{3} \log \left (x\right ) + 3 \, x^{3}}{3 \, {\left (x - 1\right )}}\right )} \]
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Time = 0.44 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {e^{\frac {x^{4} - x^{3} e^{x^{2}} - x^{3} \log {\left (x \right )} + 3 x^{3}}{3 x - 3}}}{5} \]
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\[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\int { \frac {{\left (3 \, x^{4} + x^{3} - 8 \, x^{2} - {\left (2 \, x^{5} - 2 \, x^{4} + 2 \, x^{3} - 3 \, x^{2}\right )} e^{\left (x^{2}\right )} - {\left (2 \, x^{3} - 3 \, x^{2}\right )} \log \left (x\right )\right )} e^{\left (\frac {x^{4} - x^{3} e^{\left (x^{2}\right )} - x^{3} \log \left (x\right ) + 3 \, x^{3}}{3 \, {\left (x - 1\right )}}\right )}}{15 \, {\left (x^{2} - 2 \, x + 1\right )}} \,d x } \]
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Time = 0.82 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {1}{5} \, e^{\left (\frac {x^{4}}{3 \, {\left (x - 1\right )}} - \frac {x^{3} e^{\left (x^{2}\right )}}{3 \, {\left (x - 1\right )}} - \frac {x^{3} \log \left (x\right )}{3 \, {\left (x - 1\right )}} + \frac {x^{3}}{x - 1}\right )} \]
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Time = 11.64 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.70 \[ \int \frac {e^{\frac {3 x^3-e^{x^2} x^3+x^4-x^3 \log (x)}{-3+3 x}} \left (-8 x^2+x^3+3 x^4+e^{x^2} \left (3 x^2-2 x^3+2 x^4-2 x^5\right )+\left (3 x^2-2 x^3\right ) \log (x)\right )}{15-30 x+15 x^2} \, dx=\frac {{\mathrm {e}}^{\frac {x^4}{3\,x-3}}\,{\mathrm {e}}^{-\frac {x^3\,{\mathrm {e}}^{x^2}}{3\,x-3}}\,{\mathrm {e}}^{\frac {x^3}{x-1}}}{5\,x^{\frac {x^3}{3\,x-3}}} \]
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