Integrand size = 53, antiderivative size = 29 \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=\left (5-e^{2 e^{-x^4+\frac {4+3 x}{x}}}\right ) x^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(29)=58\).
Time = 0.04 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.14, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2326} \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=5 x^2+\frac {4 e^{2 e^{\frac {-x^5+3 x+4}{x}}} \left (x^5+1\right )}{\frac {3-5 x^4}{x}-\frac {-x^5+3 x+4}{x^2}} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = 5 x^2+\int e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right ) \, dx \\ & = 5 x^2+\frac {4 e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (1+x^5\right )}{\frac {3-5 x^4}{x}-\frac {4+3 x-x^5}{x^2}} \\ \end{align*}
Time = 0.40 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=-\left (\left (-5+e^{2 e^{3+\frac {4}{x}-x^4}}\right ) x^2\right ) \]
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Time = 3.98 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00
method | result | size |
default | \(-x^{2} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {x^{5}-3 x -4}{x}}}+5 x^{2}\) | \(29\) |
risch | \(-x^{2} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {x^{5}-3 x -4}{x}}}+5 x^{2}\) | \(29\) |
parallelrisch | \(\frac {-{\mathrm e}^{2 \,{\mathrm e}^{\frac {-x^{5}+3 x +4}{x}}} x^{4}+5 x^{4}}{x^{2}}\) | \(37\) |
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Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=-x^{2} e^{\left (2 \, e^{\left (-\frac {x^{5} - 3 \, x - 4}{x}\right )}\right )} + 5 \, x^{2} \]
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Time = 0.77 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=- x^{2} e^{2 e^{\frac {- x^{5} + 3 x + 4}{x}}} + 5 x^{2} \]
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\[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=\int { 2 \, {\left (4 \, {\left (x^{5} + 1\right )} e^{\left (-\frac {x^{5} - e^{\left (\log \left (3\right ) + \log \left (x\right )\right )} - 4}{x}\right )} - x\right )} e^{\left (2 \, e^{\left (-\frac {x^{5} - e^{\left (\log \left (3\right ) + \log \left (x\right )\right )} - 4}{x}\right )}\right )} + 10 \, x \,d x } \]
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\[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=\int { 2 \, {\left (4 \, {\left (x^{5} + 1\right )} e^{\left (-\frac {x^{5} - e^{\left (\log \left (3\right ) + \log \left (x\right )\right )} - 4}{x}\right )} - x\right )} e^{\left (2 \, e^{\left (-\frac {x^{5} - e^{\left (\log \left (3\right ) + \log \left (x\right )\right )} - 4}{x}\right )}\right )} + 10 \, x \,d x } \]
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Time = 12.69 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \left (10 x+e^{2 e^{\frac {4+3 x-x^5}{x}}} \left (-2 x+e^{\frac {4+3 x-x^5}{x}} \left (8+8 x^5\right )\right )\right ) \, dx=-x^2\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^3\,{\mathrm {e}}^{4/x}\,{\mathrm {e}}^{-x^4}}-5\right ) \]
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