Integrand size = 47, antiderivative size = 21 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=\frac {1}{2} e^{-\frac {3}{x}-4 x-x^2} x \]
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Leaf count is larger than twice the leaf count of optimal. \(47\) vs. \(2(21)=42\).
Time = 0.19 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.24, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {6820, 12, 2326} \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=-\frac {e^{-x^2-4 x-\frac {3}{x}} \left (-2 x^3-4 x^2+3\right )}{2 x \left (-\frac {3}{x^2}+2 x+4\right )} \]
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Rule 12
Rule 2326
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{-\frac {3}{x}-4 x-x^2} \left (3+x-4 x^2-2 x^3\right )}{2 x} \, dx \\ & = \frac {1}{2} \int \frac {e^{-\frac {3}{x}-4 x-x^2} \left (3+x-4 x^2-2 x^3\right )}{x} \, dx \\ & = -\frac {e^{-\frac {3}{x}-4 x-x^2} \left (3-4 x^2-2 x^3\right )}{2 x \left (4-\frac {3}{x^2}+2 x\right )} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=\frac {1}{2} e^{-\frac {3+4 x^2+x^3}{x}} x \]
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Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{-\frac {x^{3}+4 x^{2}+3}{x}}}{2}\) | \(20\) |
gosper | \({\mathrm e}^{\frac {-x \ln \left (2 x \right )+2 x \ln \left (x \right )-x^{3}-4 x^{2}-3}{x}}\) | \(30\) |
parallelrisch | \({\mathrm e}^{\frac {-x \ln \left (2 x \right )+2 x \ln \left (x \right )-x^{3}-4 x^{2}-3}{x}}\) | \(30\) |
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=e^{\left (-\frac {x^{3} + 4 \, x^{2} + x \log \left (2\right ) - x \log \left (x\right ) + 3}{x}\right )} \]
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Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=e^{\frac {- x^{3} - 4 x^{2} - x \left (\log {\left (x \right )} + \log {\left (2 \right )}\right ) + 2 x \log {\left (x \right )} - 3}{x}} \]
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Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=\frac {1}{2} \, x e^{\left (-x^{2} - 4 \, x - \frac {3}{x}\right )} \]
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Time = 0.25 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.19 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=e^{\left (-x^{2} - 4 \, x - \frac {3}{x} - \log \left (2 \, x\right ) + 2 \, \log \left (x\right )\right )} \]
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Time = 9.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {e^{\frac {-3-4 x^2-x^3+2 x \log (x)-x \log (2 x)}{x}} \left (3+x-4 x^2-2 x^3\right )}{x^2} \, dx=\frac {x\,{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{-\frac {3}{x}}}{2} \]
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