Integrand size = 246, antiderivative size = 23 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\left (-1+\frac {9 e^{4 x^8}}{\log ^4\left (-3+(4+x)^2\right )}\right )^4 \]
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Time = 1.46 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6820, 12, 6844, 32} \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\left (1-\frac {9 e^{4 x^8}}{\log ^4\left (x^2+8 x+13\right )}\right )^4 \]
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Rule 12
Rule 32
Rule 6820
Rule 6844
Rubi steps \begin{align*} \text {integral}& = \int \frac {288 e^{4 x^8} \left (-4-x+4 x^7 \left (13+8 x+x^2\right ) \log \left (13+8 x+x^2\right )\right ) \left (9 e^{4 x^8}-\log ^4\left (13+8 x+x^2\right )\right )^3}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx \\ & = 288 \int \frac {e^{4 x^8} \left (-4-x+4 x^7 \left (13+8 x+x^2\right ) \log \left (13+8 x+x^2\right )\right ) \left (9 e^{4 x^8}-\log ^4\left (13+8 x+x^2\right )\right )^3}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx \\ & = 36 \text {Subst}\left (\int (-1+9 x)^3 \, dx,x,\frac {e^{4 x^8}}{\log ^4\left (13+8 x+x^2\right )}\right ) \\ & = \left (1-\frac {9 e^{4 x^8}}{\log ^4\left (13+8 x+x^2\right )}\right )^4 \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(23)=46\).
Time = 0.09 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.61 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\frac {9 e^{4 x^8} \left (729 e^{12 x^8}-324 e^{8 x^8} \log ^4\left (13+8 x+x^2\right )+54 e^{4 x^8} \log ^8\left (13+8 x+x^2\right )-4 \log ^{12}\left (13+8 x+x^2\right )\right )}{\log ^{16}\left (13+8 x+x^2\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs. \(2(22)=44\).
Time = 22.38 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.48
method | result | size |
risch | \(\frac {9 \,{\mathrm e}^{4 x^{8}} \left (729 \,{\mathrm e}^{12 x^{8}}-324 \,{\mathrm e}^{8 x^{8}} \ln \left (x^{2}+8 x +13\right )^{4}+54 \,{\mathrm e}^{4 x^{8}} \ln \left (x^{2}+8 x +13\right )^{8}-4 \ln \left (x^{2}+8 x +13\right )^{12}\right )}{\ln \left (x^{2}+8 x +13\right )^{16}}\) | \(80\) |
parallelrisch | \(-\frac {-104976 \,{\mathrm e}^{16 x^{8}}+46656 \,{\mathrm e}^{12 x^{8}} \ln \left (x^{2}+8 x +13\right )^{4}-7776 \,{\mathrm e}^{8 x^{8}} \ln \left (x^{2}+8 x +13\right )^{8}+576 \,{\mathrm e}^{4 x^{8}} \ln \left (x^{2}+8 x +13\right )^{12}}{16 \ln \left (x^{2}+8 x +13\right )^{16}}\) | \(80\) |
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (22) = 44\).
Time = 0.25 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=-\frac {9 \, {\left (4 \, e^{\left (4 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{12} - 54 \, e^{\left (8 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{8} + 324 \, e^{\left (12 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{4} - 729 \, e^{\left (16 \, x^{8}\right )}\right )}}{\log \left (x^{2} + 8 \, x + 13\right )^{16}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (20) = 40\).
Time = 0.34 (sec) , antiderivative size = 92, normalized size of antiderivative = 4.00 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\frac {6561 e^{16 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{24} - 2916 e^{12 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{28} + 486 e^{8 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{32} - 36 e^{4 x^{8}} \log {\left (x^{2} + 8 x + 13 \right )}^{36}}{\log {\left (x^{2} + 8 x + 13 \right )}^{40}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (22) = 44\).
Time = 1.88 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.43 \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=-\frac {9 \, {\left (4 \, e^{\left (4 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{12} - 54 \, e^{\left (8 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{8} + 324 \, e^{\left (12 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{4} - 729 \, e^{\left (16 \, x^{8}\right )}\right )}}{\log \left (x^{2} + 8 \, x + 13\right )^{16}} \]
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Timed out. \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx=\text {Hanged} \]
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