Integrand size = 140, antiderivative size = 22 \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=x+\left (5+x+\left (-2+e^{\frac {4}{\log (x)}}+47 x\right )^2\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(87\) vs. \(2(22)=44\).
Time = 0.99 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95, number of steps used = 7, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6874, 2240, 2326} \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=4879681 x^4-826166 x^3+74731 x^2+2 \left (6627 x^2-563 x+17\right ) e^{\frac {8}{\log (x)}}-4 \left (-103823 x^3+13207 x^2-797 x+18\right ) e^{\frac {4}{\log (x)}}-3365 x+e^{\frac {16}{\log (x)}}-4 (2-47 x) e^{\frac {12}{\log (x)}} \]
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Rule 2240
Rule 2326
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (-3365+149462 x-2478498 x^2+19518724 x^3-\frac {16 e^{\frac {16}{\log (x)}}}{x \log ^2(x)}+\frac {4 e^{\frac {12}{\log (x)}} \left (24-564 x+47 x \log ^2(x)\right )}{x \log ^2(x)}+\frac {2 e^{\frac {8}{\log (x)}} \left (-136+4504 x-53016 x^2-563 x \log ^2(x)+13254 x^2 \log ^2(x)\right )}{x \log ^2(x)}+\frac {4 e^{\frac {4}{\log (x)}} \left (72-3188 x+52828 x^2-415292 x^3+797 x \log ^2(x)-26414 x^2 \log ^2(x)+311469 x^3 \log ^2(x)\right )}{x \log ^2(x)}\right ) \, dx \\ & = -3365 x+74731 x^2-826166 x^3+4879681 x^4+2 \int \frac {e^{\frac {8}{\log (x)}} \left (-136+4504 x-53016 x^2-563 x \log ^2(x)+13254 x^2 \log ^2(x)\right )}{x \log ^2(x)} \, dx+4 \int \frac {e^{\frac {12}{\log (x)}} \left (24-564 x+47 x \log ^2(x)\right )}{x \log ^2(x)} \, dx+4 \int \frac {e^{\frac {4}{\log (x)}} \left (72-3188 x+52828 x^2-415292 x^3+797 x \log ^2(x)-26414 x^2 \log ^2(x)+311469 x^3 \log ^2(x)\right )}{x \log ^2(x)} \, dx-16 \int \frac {e^{\frac {16}{\log (x)}}}{x \log ^2(x)} \, dx \\ & = -4 e^{\frac {12}{\log (x)}} (2-47 x)-3365 x+74731 x^2-826166 x^3+4879681 x^4+2 e^{\frac {8}{\log (x)}} \left (17-563 x+6627 x^2\right )-4 e^{\frac {4}{\log (x)}} \left (18-797 x+13207 x^2-103823 x^3\right )-16 \text {Subst}\left (\int \frac {e^{16/x}}{x^2} \, dx,x,\log (x)\right ) \\ & = e^{\frac {16}{\log (x)}}-4 e^{\frac {12}{\log (x)}} (2-47 x)-3365 x+74731 x^2-826166 x^3+4879681 x^4+2 e^{\frac {8}{\log (x)}} \left (17-563 x+6627 x^2\right )-4 e^{\frac {4}{\log (x)}} \left (18-797 x+13207 x^2-103823 x^3\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(87\) vs. \(2(22)=44\).
Time = 0.42 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=e^{\frac {16}{\log (x)}}-e^{\frac {12}{\log (x)}} (8-188 x)-3365 x+74731 x^2-826166 x^3+4879681 x^4-e^{\frac {8}{\log (x)}} (-34-2 x (-563+6627 x))-e^{\frac {4}{\log (x)}} \left (72-4 x \left (797-13207 x+103823 x^2\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(21)=42\).
Time = 0.40 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.68
method | result | size |
risch | \(4879681 x^{4}+{\mathrm e}^{\frac {16}{\ln \left (x \right )}}-826166 x^{3}+74731 x^{2}-3365 x +\left (-8+188 x \right ) {\mathrm e}^{\frac {12}{\ln \left (x \right )}}+\left (13254 x^{2}-1126 x +34\right ) {\mathrm e}^{\frac {8}{\ln \left (x \right )}}+\left (415292 x^{3}-52828 x^{2}+3188 x -72\right ) {\mathrm e}^{\frac {4}{\ln \left (x \right )}}\) | \(81\) |
parallelrisch | \(415292 \,{\mathrm e}^{\frac {4}{\ln \left (x \right )}} x^{3}+4879681 x^{4}-52828 \,{\mathrm e}^{\frac {4}{\ln \left (x \right )}} x^{2}+13254 \,{\mathrm e}^{\frac {8}{\ln \left (x \right )}} x^{2}-826166 x^{3}+3188 \,{\mathrm e}^{\frac {4}{\ln \left (x \right )}} x +188 \,{\mathrm e}^{\frac {12}{\ln \left (x \right )}} x -1126 \,{\mathrm e}^{\frac {8}{\ln \left (x \right )}} x +74731 x^{2}-72 \,{\mathrm e}^{\frac {4}{\ln \left (x \right )}}+{\mathrm e}^{\frac {16}{\ln \left (x \right )}}-8 \,{\mathrm e}^{\frac {12}{\ln \left (x \right )}}+34 \,{\mathrm e}^{\frac {8}{\ln \left (x \right )}}-3365 x\) | \(132\) |
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Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (21) = 42\).
Time = 0.34 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.77 \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=4879681 \, x^{4} - 826166 \, x^{3} + 74731 \, x^{2} + 4 \, {\left (47 \, x - 2\right )} e^{\frac {12}{\log \left (x\right )}} + 2 \, {\left (6627 \, x^{2} - 563 \, x + 17\right )} e^{\frac {8}{\log \left (x\right )}} + 4 \, {\left (103823 \, x^{3} - 13207 \, x^{2} + 797 \, x - 18\right )} e^{\frac {4}{\log \left (x\right )}} - 3365 \, x + e^{\frac {16}{\log \left (x\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (19) = 38\).
Time = 2.11 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.41 \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=4879681 x^{4} - 826166 x^{3} + 74731 x^{2} - 3365 x + \left (188 x - 8\right ) e^{\frac {12}{\log {\left (x \right )}}} + \left (13254 x^{2} - 1126 x + 34\right ) e^{\frac {8}{\log {\left (x \right )}}} + \left (415292 x^{3} - 52828 x^{2} + 3188 x - 72\right ) e^{\frac {4}{\log {\left (x \right )}}} + e^{\frac {16}{\log {\left (x \right )}}} \]
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\[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=\int { \frac {{\left (19518724 \, x^{4} - 2478498 \, x^{3} + 149462 \, x^{2} - 3365 \, x\right )} \log \left (x\right )^{2} + 4 \, {\left (47 \, x \log \left (x\right )^{2} - 564 \, x + 24\right )} e^{\frac {12}{\log \left (x\right )}} + 2 \, {\left ({\left (13254 \, x^{2} - 563 \, x\right )} \log \left (x\right )^{2} - 53016 \, x^{2} + 4504 \, x - 136\right )} e^{\frac {8}{\log \left (x\right )}} - 4 \, {\left (415292 \, x^{3} - {\left (311469 \, x^{3} - 26414 \, x^{2} + 797 \, x\right )} \log \left (x\right )^{2} - 52828 \, x^{2} + 3188 \, x - 72\right )} e^{\frac {4}{\log \left (x\right )}} - 16 \, e^{\frac {16}{\log \left (x\right )}}}{x \log \left (x\right )^{2}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (21) = 42\).
Time = 0.26 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.41 \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=4879681 \, x^{4} + 415292 \, x^{3} e^{\frac {4}{\log \left (x\right )}} - 826166 \, x^{3} + 13254 \, x^{2} e^{\frac {8}{\log \left (x\right )}} - 52828 \, x^{2} e^{\frac {4}{\log \left (x\right )}} + 74731 \, x^{2} + 188 \, x e^{\frac {12}{\log \left (x\right )}} - 1126 \, x e^{\frac {8}{\log \left (x\right )}} + 3188 \, x e^{\frac {4}{\log \left (x\right )}} - 3365 \, x + e^{\frac {16}{\log \left (x\right )}} - 8 \, e^{\frac {12}{\log \left (x\right )}} + 34 \, e^{\frac {8}{\log \left (x\right )}} - 72 \, e^{\frac {4}{\log \left (x\right )}} \]
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Timed out. \[ \int \frac {-16 e^{\frac {16}{\log (x)}}+\left (-3365 x+149462 x^2-2478498 x^3+19518724 x^4\right ) \log ^2(x)+e^{\frac {12}{\log (x)}} \left (96-2256 x+188 x \log ^2(x)\right )+e^{\frac {8}{\log (x)}} \left (-272+9008 x-106032 x^2+\left (-1126 x+26508 x^2\right ) \log ^2(x)\right )+e^{\frac {4}{\log (x)}} \left (288-12752 x+211312 x^2-1661168 x^3+\left (3188 x-105656 x^2+1245876 x^3\right ) \log ^2(x)\right )}{x \log ^2(x)} \, dx=-\int \frac {16\,{\mathrm {e}}^{\frac {16}{\ln \left (x\right )}}-{\mathrm {e}}^{\frac {4}{\ln \left (x\right )}}\,\left ({\ln \left (x\right )}^2\,\left (1245876\,x^3-105656\,x^2+3188\,x\right )-12752\,x+211312\,x^2-1661168\,x^3+288\right )+{\ln \left (x\right )}^2\,\left (-19518724\,x^4+2478498\,x^3-149462\,x^2+3365\,x\right )-{\mathrm {e}}^{\frac {12}{\ln \left (x\right )}}\,\left (188\,x\,{\ln \left (x\right )}^2-2256\,x+96\right )+{\mathrm {e}}^{\frac {8}{\ln \left (x\right )}}\,\left ({\ln \left (x\right )}^2\,\left (1126\,x-26508\,x^2\right )-9008\,x+106032\,x^2+272\right )}{x\,{\ln \left (x\right )}^2} \,d x \]
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