Integrand size = 118, antiderivative size = 18 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=e^{\left (3+\frac {x}{2}+x^{-2+x}\right )^2}+x \]
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\[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=\int \frac {2 x^5+\exp \left (\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}\right ) \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {2 x^5+\exp \left (\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}\right ) \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{x^5} \, dx \\ & = \frac {1}{2} \int \left (2+6 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x+4 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} (-2+x+x \log (x))+2 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \left (-12+5 x+x^2+6 x \log (x)+x^2 \log (x)\right )\right ) \, dx \\ & = x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} (-2+x+x \log (x)) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \left (-12+5 x+x^2+6 x \log (x)+x^2 \log (x)\right ) \, dx \\ & = x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int \left (-2 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \log (x)\right ) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx+\int \left (-12 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x}+5 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x}+6 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \log (x)+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \log (x)\right ) \, dx \\ & = x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \log (x) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx-4 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} \, dx+5 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx+6 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \log (x) \, dx-12 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \log (x) \, dx \\ & = x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx-2 \int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx}{x} \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx-4 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} \, dx+5 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx-6 \int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx}{x} \, dx-12 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \, dx+\log (x) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx+(2 \log (x)) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx+(6 \log (x)) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx-\int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx}{x} \, dx \\ \end{align*}
Time = 2.91 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.78 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=e^{9+3 x+\frac {x^2}{4}+x^{-4+2 x}+x^{-2+x} (6+x)}+x \]
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Time = 2.73 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.39
method | result | size |
risch | \(x +{\mathrm e}^{\frac {\left (x^{3}+6 x^{2}+2 x^{x}\right )^{2}}{4 x^{4}}}\) | \(25\) |
parallelrisch | \(x +{\mathrm e}^{\frac {4 \,{\mathrm e}^{2 x \ln \left (x \right )}+\left (4 x^{3}+24 x^{2}\right ) {\mathrm e}^{x \ln \left (x \right )}+x^{6}+12 x^{5}+36 x^{4}}{4 x^{4}}}\) | \(49\) |
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Leaf count of result is larger than twice the leaf count of optimal. 43 vs. \(2 (18) = 36\).
Time = 0.25 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.39 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=x + e^{\left (\frac {x^{6} + 12 \, x^{5} + 36 \, x^{4} + 4 \, {\left (x^{3} + 6 \, x^{2}\right )} x^{x} + 4 \, x^{2 \, x}}{4 \, x^{4}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (19) = 38\).
Time = 0.46 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.67 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=x + e^{\frac {\frac {x^{6}}{4} + 3 x^{5} + 9 x^{4} + \frac {\left (4 x^{3} + 24 x^{2}\right ) e^{x \log {\left (x \right )}}}{4} + e^{2 x \log {\left (x \right )}}}{x^{4}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 37 vs. \(2 (18) = 36\).
Time = 0.33 (sec) , antiderivative size = 37, normalized size of antiderivative = 2.06 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=x + e^{\left (\frac {1}{4} \, x^{2} + 3 \, x + \frac {x^{x}}{x} + \frac {6 \, x^{x}}{x^{2}} + \frac {x^{2 \, x}}{x^{4}} + 9\right )} \]
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Timed out. \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=\text {Timed out} \]
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Time = 13.25 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.33 \[ \int \frac {2 x^5+e^{\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}} \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx=x+{\left ({\mathrm {e}}^{x^2}\right )}^{1/4}\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{\frac {x^{2\,x}}{x^4}}\,{\mathrm {e}}^9\,{\mathrm {e}}^{\frac {x^x}{x}}\,{\mathrm {e}}^{\frac {6\,x^x}{x^2}} \]
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