Integrand size = 216, antiderivative size = 31 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+\frac {\left (e^{\frac {1}{2} x \left (2-e^{25}+x-\log (x)\right )}+x\right )^4}{x^4} \]
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\[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-1+2 e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+6 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+6 e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )+2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right )\right ) \, dx \\ & = -x+2 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+2 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+6 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx+6 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \left (-2+\left (1-e^{25}\right ) x+2 x^2-x \log (x)\right ) \, dx \\ & = -x+2 \int \left (-2 e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x}+e^{2 x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-4-2 x}+2 e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x}-e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \log (x)\right ) \, dx+2 \int \left (-2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}}+e^{\frac {1}{2} x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-1-\frac {x}{2}}+2 e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2}-e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \log (x)\right ) \, dx+6 \int \left (-2 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}}+e^{\frac {3}{2} x \left (2-e^{25}+x\right )} \left (1-e^{25}\right ) x^{-3-\frac {3 x}{2}}+2 e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}}-e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \log (x)\right ) \, dx+6 \int \left (-2 e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x}+e^{\left (2-e^{25}\right ) x+x^2} \left (1-e^{25}\right ) x^{-2-x}+2 e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x}-e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \log (x)\right ) \, dx \\ & = -x-2 \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \log (x) \, dx-2 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \log (x) \, dx-4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \, dx+4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x} \, dx-4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \, dx+4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2} \, dx-6 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \log (x) \, dx-6 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \log (x) \, dx-12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \, dx+12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}} \, dx-12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \, dx+12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx \\ & = -x+2 \int \frac {\int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx}{x} \, dx+2 \int \frac {\int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx}{x} \, dx-4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-5-2 x} \, dx+4 \int e^{2 x \left (2-e^{25}+x\right )} x^{-3-2 x} \, dx-4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {x}{2}} \, dx+4 \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-x/2} \, dx+6 \int \frac {\int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx}{x} \, dx+6 \int \frac {\int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx}{x} \, dx-12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-4-\frac {3 x}{2}} \, dx+12 \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-2-\frac {3 x}{2}} \, dx-12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-3-x} \, dx+12 \int e^{\left (2-e^{25}\right ) x+x^2} x^{-1-x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx+\left (2 \left (1-e^{25}\right )\right ) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx+\left (6 \left (1-e^{25}\right )\right ) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx-(2 \log (x)) \int e^{2 x \left (2-e^{25}+x\right )} x^{-4-2 x} \, dx-(2 \log (x)) \int e^{\frac {1}{2} x \left (2-e^{25}+x\right )} x^{-1-\frac {x}{2}} \, dx-(6 \log (x)) \int e^{\frac {3}{2} x \left (2-e^{25}+x\right )} x^{-3-\frac {3 x}{2}} \, dx-(6 \log (x)) \int e^{\left (2-e^{25}\right ) x+x^2} x^{-2-x} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(31)=62\).
Time = 4.34 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.65 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x+e^{-2 \left (-2+e^{25}\right ) x+2 x^2} x^{-4-2 x}+4 e^{-\frac {3}{2} \left (-2+e^{25}\right ) x+\frac {3 x^2}{2}} x^{-3-\frac {3 x}{2}}+6 e^{-\left (\left (-2+e^{25}\right ) x\right )+x^2} x^{-2-x}+4 e^{-\frac {1}{2} \left (-2+e^{25}\right ) x+\frac {x^2}{2}} x^{-1-\frac {x}{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(27)=54\).
Time = 2.49 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.65
method | result | size |
parallelrisch | \(\frac {-x^{5}+4 \,{\mathrm e}^{-\frac {x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x^{3}+6 \,{\mathrm e}^{-x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )} x^{2}+4 \,{\mathrm e}^{-\frac {3 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}{2}} x +{\mathrm e}^{-2 x \left (\ln \left (x \right )+{\mathrm e}^{25}-x -2\right )}}{x^{4}}\) | \(82\) |
risch | \(-x +\frac {x^{-2 x} {\mathrm e}^{-2 x \left ({\mathrm e}^{25}-x -2\right )}}{x^{4}}+\frac {4 x^{-\frac {3 x}{2}} {\mathrm e}^{-\frac {3 x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x^{3}}+\frac {6 x^{-x} {\mathrm e}^{-x \left ({\mathrm e}^{25}-x -2\right )}}{x^{2}}+\frac {4 x^{-\frac {x}{2}} {\mathrm e}^{-\frac {x \left ({\mathrm e}^{25}-x -2\right )}{2}}}{x}\) | \(94\) |
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Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (22) = 44\).
Time = 0.23 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.74 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=- x + \frac {4 x^{9} e^{\frac {x^{2}}{2} - \frac {x \log {\left (x \right )}}{2} - \frac {x e^{25}}{2} + x} + 6 x^{8} e^{x^{2} - x \log {\left (x \right )} - x e^{25} + 2 x} + 4 x^{7} e^{\frac {3 x^{2}}{2} - \frac {3 x \log {\left (x \right )}}{2} - \frac {3 x e^{25}}{2} + 3 x} + x^{6} e^{2 x^{2} - 2 x \log {\left (x \right )} - 2 x e^{25} + 4 x}}{x^{10}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (27) = 54\).
Time = 0.29 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.19 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-x + \frac {4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {3}{2} \, x \log \left (x\right ) + x\right )} + 6 \, x^{2} e^{\left (x^{2} - x e^{25} + x \log \left (x\right ) + 2 \, x\right )} + 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} + \frac {1}{2} \, x \log \left (x\right ) + 3 \, x\right )} + e^{\left (2 \, x^{2} - 2 \, x e^{25} + 4 \, x\right )}}{x^{4} x^{2 \, x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.37 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=-\frac {x^{5} - 4 \, x^{3} e^{\left (\frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} - \frac {1}{2} \, x \log \left (x\right ) + x\right )} - 6 \, x^{2} e^{\left (x^{2} - x e^{25} - x \log \left (x\right ) + 2 \, x\right )} - 4 \, x e^{\left (\frac {3}{2} \, x^{2} - \frac {3}{2} \, x e^{25} - \frac {3}{2} \, x \log \left (x\right ) + 3 \, x\right )} - e^{\left (2 \, x^{2} - 2 \, x e^{25} - 2 \, x \log \left (x\right ) + 4 \, x\right )}}{x^{4}} \]
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Time = 10.25 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.26 \[ \int \frac {-x^5+e^{2 \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4+2 x-2 e^{25} x+4 x^2-2 x \log (x)\right )+e^{\frac {3}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-12 x+6 x^2-6 e^{25} x^2+12 x^3-6 x^2 \log (x)\right )+e^{2 x-e^{25} x+x^2-x \log (x)} \left (-12 x^2+6 x^3-6 e^{25} x^3+12 x^4-6 x^3 \log (x)\right )+e^{\frac {1}{2} \left (2 x-e^{25} x+x^2-x \log (x)\right )} \left (-4 x^3+2 x^4-2 e^{25} x^4+4 x^5-2 x^4 \log (x)\right )}{x^5} \, dx=\frac {4\,{\mathrm {e}}^{3\,x-\frac {3\,x\,{\mathrm {e}}^{25}}{2}-\frac {3\,x\,\ln \left (x\right )}{2}+\frac {3\,x^2}{2}}}{x^3}-x+\frac {4\,{\mathrm {e}}^{x-\frac {x\,{\mathrm {e}}^{25}}{2}-\frac {x\,\ln \left (x\right )}{2}+\frac {x^2}{2}}}{x}+\frac {6\,{\mathrm {e}}^{2\,x-x\,{\mathrm {e}}^{25}+x^2}}{x^x\,x^2}+\frac {{\mathrm {e}}^{4\,x-2\,x\,{\mathrm {e}}^{25}+2\,x^2}}{x^{2\,x}\,x^4} \]
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