Integrand size = 206, antiderivative size = 31 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\left (\frac {e^6}{3}-x-x^2\right )^2 (3-x+\log (-7+\log (-4+x))) \]
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\[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (e^6-3 x-3 x^2\right ) \left (-504 \left (1+\frac {3 e^6}{56}\right )-633 \left (1-\frac {7 e^6}{633}\right ) x+606 x^2-105 x^3+42 \left (-4-7 x+2 x^2\right ) \log (-7+\log (-4+x))-(-4+x) \log (-4+x) \left (18+e^6+27 x-15 x^2+6 (1+2 x) \log (-7+\log (-4+x))\right )\right )}{9 (4-x) (7-\log (-4+x))} \, dx \\ & = \frac {1}{9} \int \frac {\left (e^6-3 x-3 x^2\right ) \left (-504 \left (1+\frac {3 e^6}{56}\right )-633 \left (1-\frac {7 e^6}{633}\right ) x+606 x^2-105 x^3+42 \left (-4-7 x+2 x^2\right ) \log (-7+\log (-4+x))-(-4+x) \log (-4+x) \left (18+e^6+27 x-15 x^2+6 (1+2 x) \log (-7+\log (-4+x))\right )\right )}{(4-x) (7-\log (-4+x))} \, dx \\ & = \frac {1}{9} \int \left (-\frac {9 \left (56+3 e^6\right ) \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))}+\frac {\left (-633+7 e^6\right ) x \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))}-\frac {606 x^2 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))}+\frac {105 x^3 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))}-\frac {18 \left (1+\frac {e^6}{18}\right ) \left (e^6-3 x-3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}+\frac {27 x \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}-\frac {15 x^2 \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}+6 (1+2 x) \left (-e^6+3 x+3 x^2\right ) \log (-7+\log (-4+x))\right ) \, dx \\ & = \frac {2}{3} \int (1+2 x) \left (-e^6+3 x+3 x^2\right ) \log (-7+\log (-4+x)) \, dx-\frac {5}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+3 \int \frac {x \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+\frac {35}{3} \int \frac {x^3 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx-\frac {202}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx+\left (-56-3 e^6\right ) \int \frac {e^6-3 x-3 x^2}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (-18-e^6\right ) \int \frac {\left (e^6-3 x-3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+\frac {1}{9} \left (-633+7 e^6\right ) \int \frac {x \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx \\ & = \frac {2}{3} \int \left (-e^6 \log (-7+\log (-4+x))-\left (-3+2 e^6\right ) x \log (-7+\log (-4+x))+9 x^2 \log (-7+\log (-4+x))+6 x^3 \log (-7+\log (-4+x))\right ) \, dx-\frac {5}{3} \int \left (x^2 \left (-e^6+3 x+3 x^2\right )+\frac {7 x^2 \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+3 \int \left (x \left (-e^6+3 x+3 x^2\right )+\frac {7 x \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+\frac {35}{3} \int \left (-\frac {16 \left (-60+e^6\right )}{-7+\log (-4+x)}-\frac {64 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {4 \left (-60+e^6\right ) x}{-7+\log (-4+x)}-\frac {\left (-60+e^6\right ) x^2}{-7+\log (-4+x)}+\frac {15 x^3}{-7+\log (-4+x)}+\frac {3 x^4}{-7+\log (-4+x)}\right ) \, dx-\frac {202}{3} \int \left (-\frac {4 \left (-60+e^6\right )}{-7+\log (-4+x)}-\frac {16 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {\left (-60+e^6\right ) x}{-7+\log (-4+x)}+\frac {15 x^2}{-7+\log (-4+x)}+\frac {3 x^3}{-7+\log (-4+x)}\right ) \, dx+\left (-56-3 e^6\right ) \int \left (-\frac {15}{-7+\log (-4+x)}+\frac {-60+e^6}{(-4+x) (-7+\log (-4+x))}-\frac {3 x}{-7+\log (-4+x)}\right ) \, dx+\frac {1}{9} \left (-18-e^6\right ) \int \left (e^6-3 x-3 x^2+\frac {7 \left (e^6-3 x-3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+\frac {1}{9} \left (-633+7 e^6\right ) \int \left (\frac {-168+e^6}{-7+\log (-4+x)}+\frac {4 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {39 (-4+x)}{-7+\log (-4+x)}-\frac {3 (-4+x)^2}{-7+\log (-4+x)}\right ) \, dx \\ & = -\frac {1}{9} e^6 \left (18+e^6\right ) x+\frac {1}{6} \left (18+e^6\right ) x^2+\frac {1}{9} \left (18+e^6\right ) x^3-\frac {5}{3} \int x^2 \left (-e^6+3 x+3 x^2\right ) \, dx+3 \int x \left (-e^6+3 x+3 x^2\right ) \, dx+4 \int x^3 \log (-7+\log (-4+x)) \, dx+6 \int x^2 \log (-7+\log (-4+x)) \, dx-\frac {35}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)} \, dx+21 \int \frac {x \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)} \, dx+35 \int \frac {x^4}{-7+\log (-4+x)} \, dx+175 \int \frac {x^3}{-7+\log (-4+x)} \, dx-202 \int \frac {x^3}{-7+\log (-4+x)} \, dx-1010 \int \frac {x^2}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (2 e^6\right ) \int \log (-7+\log (-4+x)) \, dx+\frac {1}{3} \left (633-7 e^6\right ) \int \frac {(-4+x)^2}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (13 \left (633-7 e^6\right )\right ) \int \frac {-4+x}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (2 \left (3-2 e^6\right )\right ) \int x \log (-7+\log (-4+x)) \, dx+\frac {1}{3} \left (35 \left (60-e^6\right )\right ) \int \frac {x^2}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (140 \left (60-e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (202 \left (60-e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (560 \left (60-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (808 \left (60-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (2240 \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx-\frac {1}{3} \left (3232 \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (4 \left (633-7 e^6\right ) \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (\left (633-7 e^6\right ) \left (168-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx-\frac {1}{9} \left (7 \left (18+e^6\right )\right ) \int \frac {e^6-3 x-3 x^2}{-7+\log (-4+x)} \, dx+\left (3 \left (56+3 e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx+\left (15 \left (56+3 e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx+\left (\left (60-e^6\right ) \left (56+3 e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(31)=62\).
Time = 0.11 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.90 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\frac {1}{9} \left (-e^6 \left (18+e^6\right ) x-3 \left (-9+4 e^6\right ) x^2+3 \left (15+2 e^6\right ) x^3+9 x^4-9 x^5+e^{12} \log (7-\log (-4+x))-3 x (1+x) \left (2 e^6-3 x-3 x^2\right ) \log (-7+\log (-4+x))\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(30)=60\).
Time = 7.64 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.13
method | result | size |
risch | \(\frac {\left ({\mathrm e}^{6}-3 x^{2}-3 x \right )^{2} \ln \left (\ln \left (x -4\right )-7\right )}{9}-x^{5}+x^{4}+\frac {2 x^{3} {\mathrm e}^{6}}{3}+5 x^{3}-\frac {4 x^{2} {\mathrm e}^{6}}{3}+3 x^{2}-\frac {x \,{\mathrm e}^{12}}{9}-2 x \,{\mathrm e}^{6}\) | \(66\) |
parallelrisch | \(-\frac {x \,{\mathrm e}^{12}}{9}+\frac {{\mathrm e}^{12} \ln \left (\ln \left (x -4\right )-7\right )}{9}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x^{2}}{3}-x^{5}+\ln \left (\ln \left (x -4\right )-7\right ) x^{4}-\frac {8 \,{\mathrm e}^{12}}{9}-\frac {4 x^{2} {\mathrm e}^{6}}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x}{3}+x^{4}+2 \ln \left (\ln \left (x -4\right )-7\right ) x^{3}-2 x \,{\mathrm e}^{6}+5 x^{3}+\ln \left (\ln \left (x -4\right )-7\right ) x^{2}+\frac {16 \,{\mathrm e}^{6}}{3}+3 x^{2}-48\) | \(142\) |
default | \(400-2 x \,{\mathrm e}^{6}-\frac {x \,{\mathrm e}^{12}}{9}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {4 x^{2} {\mathrm e}^{6}}{3}+400 \ln \left (\ln \left (x -4\right )-7\right )+\frac {4 \,{\mathrm e}^{12}}{9}-\frac {40 \,{\mathrm e}^{6}}{3}+x^{4}+5 x^{3}+3 x^{2}-x^{5}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x^{2}}{3}+\frac {{\mathrm e}^{12} \ln \left (\ln \left (x -4\right )-7\right )}{9}+2 \left (\frac {\left (x -4\right )^{2}}{2}+4 x -16\right ) \ln \left (\ln \left (x -4\right )-7\right )+6 \left (\frac {\left (x -4\right )^{3}}{3}+4 \left (x -4\right )^{2}+16 x -64\right ) \ln \left (\ln \left (x -4\right )-7\right )+4 \left (\frac {\left (x -4\right )^{4}}{4}+4 \left (x -4\right )^{3}+24 \left (x -4\right )^{2}+64 x -256\right ) \ln \left (\ln \left (x -4\right )-7\right )\) | \(201\) |
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Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (29) = 58\).
Time = 0.31 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.45 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} + 5 \, x^{3} + 3 \, x^{2} - \frac {1}{9} \, x e^{12} + \frac {2}{3} \, {\left (x^{3} - 2 \, x^{2} - 3 \, x\right )} e^{6} + \frac {1}{9} \, {\left (9 \, x^{4} + 18 \, x^{3} + 9 \, x^{2} - 6 \, {\left (x^{2} + x\right )} e^{6} + e^{12}\right )} \log \left (\log \left (x - 4\right ) - 7\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (22) = 44\).
Time = 0.60 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=- x^{5} + x^{4} + x^{3} \cdot \left (5 + \frac {2 e^{6}}{3}\right ) + x^{2} \cdot \left (3 - \frac {4 e^{6}}{3}\right ) + x \left (- \frac {e^{12}}{9} - 2 e^{6}\right ) + \left (x^{4} + 2 x^{3} - \frac {2 x^{2} e^{6}}{3} + x^{2} - \frac {2 x e^{6}}{3} - \frac {1328}{15} + \frac {44 e^{6}}{9}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )} + \frac {\left (- 220 e^{6} + 3984 + 5 e^{12}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )}}{45} \]
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Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (29) = 58\).
Time = 0.23 (sec) , antiderivative size = 287, normalized size of antiderivative = 9.26 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} + \frac {1}{3} \, x^{3} {\left (2 \, e^{6} + 15\right )} - \frac {1}{3} \, x^{2} {\left (4 \, e^{6} - 9\right )} - \frac {8}{3} \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + \frac {4}{9} \, e^{12} \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) + 8 \, e^{6} \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {28}{3} \, e^{6} \log \left (\log \left (x - 4\right ) - 7\right )^{2} - \frac {1}{9} \, x {\left (e^{12} + 18 \, e^{6}\right )} - \frac {4}{9} \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{12} - 8 \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{6} - \frac {4}{3} \, {\left (7 \, \log \left (\log \left (x - 4\right ) - 7\right )^{2} + 2 \, \log \left (x - 4\right )\right )} e^{6} - \frac {4}{9} \, {\left (e^{12} + 12 \, e^{6}\right )} \log \left (x - 4\right ) + \frac {1}{3} \, {\left (3 \, x^{4} + 6 \, x^{3} - x^{2} {\left (2 \, e^{6} - 3\right )} - 2 \, x e^{6} - 8 \, e^{6} \log \left (x - 4\right ) + 56 \, e^{6}\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - 3 \, e^{12} \log \left (\log \left (x - 4\right ) - 7\right ) - 56 \, e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (29) = 58\).
Time = 0.31 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} \log \left (\log \left (x - 4\right ) - 7\right ) + x^{4} + \frac {2}{3} \, x^{3} e^{6} + 2 \, x^{3} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x^{2} e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 5 \, x^{3} - \frac {4}{3} \, x^{2} e^{6} + x^{2} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 3 \, x^{2} - \frac {1}{9} \, x e^{12} - 2 \, x e^{6} + \frac {1}{9} \, e^{12} \log \left (\log \left (x - 4\right ) - 7\right ) \]
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Time = 9.32 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.87 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=x^3\,\left (\frac {2\,{\mathrm {e}}^6}{3}+5\right )-x^2\,\left (\frac {4\,{\mathrm {e}}^6}{3}-3\right )-x\,\left (2\,{\mathrm {e}}^6+\frac {{\mathrm {e}}^{12}}{9}\right )-\ln \left (\ln \left (x-4\right )-7\right )\,\left (\frac {2\,x\,{\mathrm {e}}^6}{3}+\frac {x^2\,\left (2\,{\mathrm {e}}^6-3\right )}{3}-2\,x^3-x^4\right )+\frac {\ln \left (\ln \left (x-4\right )-7\right )\,{\mathrm {e}}^{12}}{9}+x^4-x^5 \]
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