Integrand size = 82, antiderivative size = 28 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=\frac {x}{3-x \left (3+\frac {e^{x+17 x^2}+x^3}{x}\right )} \]
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\[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=\int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{\left (3-e^{x+17 x^2}-3 x-x^3\right )^2} \, dx \\ & = \int \left (\frac {-1+x+34 x^2}{-3+e^{x+17 x^2}+3 x+x^3}-\frac {x \left (-6-99 x+99 x^2+x^3+34 x^4\right )}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}\right ) \, dx \\ & = \int \frac {-1+x+34 x^2}{-3+e^{x+17 x^2}+3 x+x^3} \, dx-\int \frac {x \left (-6-99 x+99 x^2+x^3+34 x^4\right )}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx \\ & = -\int \left (-\frac {6 x}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}-\frac {99 x^2}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {99 x^3}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {x^4}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {34 x^5}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}\right ) \, dx+\int \left (-\frac {1}{-3+e^{x+17 x^2}+3 x+x^3}+\frac {x}{-3+e^{x+17 x^2}+3 x+x^3}+\frac {34 x^2}{-3+e^{x+17 x^2}+3 x+x^3}\right ) \, dx \\ & = 6 \int \frac {x}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-34 \int \frac {x^5}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx+34 \int \frac {x^2}{-3+e^{x+17 x^2}+3 x+x^3} \, dx+99 \int \frac {x^2}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-99 \int \frac {x^3}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-\int \frac {x^4}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-\int \frac {1}{-3+e^{x+17 x^2}+3 x+x^3} \, dx+\int \frac {x}{-3+e^{x+17 x^2}+3 x+x^3} \, dx \\ \end{align*}
Time = 3.84 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=-\frac {x}{-3+e^{x+17 x^2}+3 x+x^3} \]
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Time = 0.12 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79
method | result | size |
risch | \(-\frac {x}{x^{3}+{\mathrm e}^{x \left (17 x +1\right )}+3 x -3}\) | \(22\) |
parallelrisch | \(-\frac {x}{x^{3}+{\mathrm e}^{x} {\mathrm e}^{17 x^{2}}+3 x -3}\) | \(23\) |
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Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=-\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \]
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Time = 0.11 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.71 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=- \frac {x}{x^{3} + 3 x + e^{x} e^{17 x^{2}} - 3} \]
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Time = 0.21 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=-\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \]
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Time = 0.28 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=-\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \]
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Time = 9.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx=-\frac {x}{3\,x+{\mathrm {e}}^{17\,x^2+x}+x^3-3} \]
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