Integrand size = 243, antiderivative size = 24 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\left (\frac {e^3}{x^2 \left (-2+x+x^5\right )}-\log (2 x)\right )^2 \] Output:
(exp(3)/x^2/(x^5+x-2)-ln(2*x))^2
Time = 5.05 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\frac {\left (e^3-x^2 \left (-2+x+x^5\right ) \log (2 x)\right )^2}{x^4 \left (-2+x+x^5\right )^2} \] Input:
Integrate[(E^6*(8 - 6*x) + E^3*(-8*x^2 + 8*x^3 - 2*x^4) + 2*x^19*Log[2*x] + (-16*x^4 + 24*x^5 - 12*x^6 + 2*x^7 + E^3*(16*x^2 - 20*x^3 + 6*x^4))*Log[ 2*x] + x^10*(-2*E^3*x^2 + (14*E^3*x^2 - 12*x^4 + 6*x^5)*Log[2*x]) + x^5*(- 14*E^6 + E^3*(8*x^2 - 4*x^3) + (24*x^4 - 24*x^5 + 6*x^6 + E^3*(-36*x^2 + 2 0*x^3))*Log[2*x]))/(-8*x^5 + 12*x^6 - 6*x^7 + x^8 + x^20 + x^10*(-6*x^5 + 3*x^6) + x^5*(12*x^5 - 12*x^6 + 3*x^7)),x]
Output:
(E^3 - x^2*(-2 + x + x^5)*Log[2*x])^2/(x^4*(-2 + x + x^5)^2)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {2 x^{19} \log (2 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+x^{10} \left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right )+x^5 \left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)+e^6 (8-6 x)}{x^{20}+x^8-6 x^7+12 x^6-8 x^5+\left (3 x^6-6 x^5\right ) x^{10}+\left (3 x^7-12 x^6+12 x^5\right ) x^5} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {2 x^{19} \log (2 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+x^{10} \left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right )+x^5 \left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)+e^6 (8-6 x)}{x^5 \left (x^{15}+3 x^{11}-6 x^{10}+3 x^7-12 x^6+12 x^5+x^3-6 x^2+12 x-8\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (-35 x^3-55 x^2-63 x-62\right ) \left (2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)\right )}{648 x^5 \left (x^4+x^3+x^2+x+2\right )}+\frac {\left (-15 x^3-20 x^2-18 x-12\right ) \left (2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)\right )}{108 x^5 \left (x^4+x^3+x^2+x+2\right )^2}+\frac {\left (-10 x^3-5 x^2+6 x+14\right ) \left (2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)\right )}{54 x^5 \left (x^4+x^3+x^2+x+2\right )^3}+\frac {35 \left (2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)\right )}{648 (x-1) x^5}-\frac {5 \left (2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)\right )}{216 (x-1)^2 x^5}+\frac {2 \log (2 x) x^{19}+\left (\left (6 x^5-12 x^4+14 e^3 x^2\right ) \log (2 x)-2 e^3 x^2\right ) x^{10}+\left (e^3 \left (8 x^2-4 x^3\right )+\left (6 x^6-24 x^5+24 x^4+e^3 \left (20 x^3-36 x^2\right )\right ) \log (2 x)-14 e^6\right ) x^5+e^6 (8-6 x)+e^3 \left (-2 x^4+8 x^3-8 x^2\right )+\left (2 x^7-12 x^6+24 x^5-16 x^4+e^3 \left (6 x^4-20 x^3+16 x^2\right )\right ) \log (2 x)}{216 (x-1)^3 x^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (e^3 \left (7 x^5+3 x-4\right )+x^2 \left (x^5+x-2\right )^2\right ) \left (e^3-x^2 \left (x^5+x-2\right ) \log (2 x)\right )}{x^5 \left (-x^5-x+2\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{x^5 \left (-x^5-x+2\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{x^5 \left (-x^5-x+2\right )^3}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle -2 \int \left (\frac {\left (35 x^3+55 x^2+63 x+62\right ) \left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{648 x^5 \left (x^4+x^3+x^2+x+2\right )}+\frac {\left (15 x^3+20 x^2+18 x+12\right ) \left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{108 x^5 \left (x^4+x^3+x^2+x+2\right )^2}+\frac {\left (10 x^3+5 x^2-6 x-14\right ) \left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{54 x^5 \left (x^4+x^3+x^2+x+2\right )^3}-\frac {35 \left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{648 (x-1) x^5}+\frac {5 \left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{216 (x-1)^2 x^5}-\frac {\left (e^3 \left (-7 x^5-3 x+4\right )-x^2 \left (-x^5-x+2\right )^2\right ) \left (\left (-x^5-x+2\right ) \log (2 x) x^2+e^3\right )}{216 (x-1)^3 x^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (\frac {5}{648} \left (2-7 e^3\right ) \log (2 x) x^7-\frac {\left (34-245 e^3\right ) \log (2 x) x^7}{4536}-\frac {1}{126} \log (2 x) x^7-\frac {5 \left (2-7 e^3\right ) x^7}{4536}+\frac {\left (34-245 e^3\right ) x^7}{31752}+\frac {x^7}{882}+\frac {5 \left (2+7 e^3\right ) \log (2 x) x^6}{1296}-\frac {35 \left (1+7 e^3\right ) \log (2 x) x^6}{3888}-\frac {5 \left (17-28 e^3\right ) \log (2 x) x^6}{3888}+\frac {5}{216} \log (2 x) x^6-\frac {5 \left (2+7 e^3\right ) x^6}{7776}+\frac {35 \left (1+7 e^3\right ) x^6}{23328}+\frac {5 \left (17-28 e^3\right ) x^6}{23328}-\frac {5 x^6}{1296}+\frac {1}{216} \left (3+14 e^3\right ) \log (2 x) x^5-\frac {\left (30+7 e^3\right ) \log (2 x) x^5}{1080}+\frac {1}{405} \left (16+7 e^3\right ) \log (2 x) x^5+\frac {7}{648} \left (11-7 e^3\right ) \log (2 x) x^5-\frac {13}{90} \log (2 x) x^5-\frac {\left (3+14 e^3\right ) x^5}{1080}+\frac {\left (30+7 e^3\right ) x^5}{5400}-\frac {\left (16+7 e^3\right ) x^5}{2025}-\frac {7 \left (11-7 e^3\right ) x^5}{3240}+\frac {13 x^5}{450}-\frac {1}{288} \left (11+7 e^3\right ) \log (2 x) x^4-\frac {35 \left (1+7 e^3\right ) \log (2 x) x^4}{2592}+\frac {\left (68-7 e^3\right ) \log (2 x) x^4}{2592}-\frac {5}{864} \left (8-21 e^3\right ) \log (2 x) x^4+\frac {31}{432} \log (2 x) x^4+\frac {\left (11+7 e^3\right ) x^4}{1152}+\frac {35 \left (1+7 e^3\right ) x^4}{10368}-\frac {\left (68-7 e^3\right ) x^4}{10368}+\frac {5 \left (8-21 e^3\right ) x^4}{3456}-\frac {31 x^4}{1728}-\frac {1}{648} \left (25+42 e^3\right ) \log (2 x) x^3+\frac {5}{324} \left (2+21 e^3\right ) \log (2 x) x^3-\frac {35 \left (1+17 e^3\right ) \log (2 x) x^3}{1944}-\frac {35}{648} \left (1-4 e^3\right ) \log (2 x) x^3+\frac {47 \left (1-7 e^3\right ) \log (2 x) x^3}{1944}+\frac {1}{18} \log (2 x) x^3+\frac {\left (25+42 e^3\right ) x^3}{1944}-\frac {5}{972} \left (2+21 e^3\right ) x^3+\frac {35 \left (1+17 e^3\right ) x^3}{5832}+\frac {35 \left (1-4 e^3\right ) x^3}{1944}-\frac {47 \left (1-7 e^3\right ) x^3}{5832}-\frac {x^3}{54}-\frac {1}{648} \left (13+40 e^3\right ) \log (2 x) x^2-\frac {1}{216} \left (9+35 e^3\right ) \log (2 x) x^2-\frac {35 \left (2-e^3\right ) \log (2 x) x^2}{1296}-\frac {5}{144} \left (2-15 e^3\right ) \log (2 x) x^2+\frac {1}{108} \left (1-35 e^3\right ) \log (2 x) x^2+\frac {19}{108} \log (2 x) x^2+\frac {\left (13+40 e^3\right ) x^2}{1296}+\frac {1}{432} \left (9+35 e^3\right ) x^2+\frac {35 \left (2-e^3\right ) x^2}{2592}+\frac {5}{288} \left (2-15 e^3\right ) x^2-\frac {1}{216} \left (1-35 e^3\right ) x^2-\frac {19 x^2}{216}-\frac {e^3 \log (2 x) x}{6 (1-x)}-\frac {1}{216} \left (12+115 e^3\right ) \log (2 x) x+\frac {35}{648} \left (4+e^3\right ) \log (2 x) x-\frac {5}{54} \left (1-11 e^3\right ) \log (2 x) x+\frac {1}{162} \left (61-14 e^3\right ) \log (2 x) x+\frac {1}{108} \left (24-49 e^3\right ) \log (2 x) x-\frac {2}{3} \log (2 x) x+\frac {1}{216} \left (12+115 e^3\right ) x-\frac {35}{648} \left (4+e^3\right ) x+\frac {5}{54} \left (1-11 e^3\right ) x-\frac {1}{162} \left (61-14 e^3\right ) x-\frac {1}{108} \left (24-49 e^3\right ) x+\frac {2 x}{3}-\frac {\left (248+35 e^3\right ) \log ^2(2 x)}{1296}-\frac {1}{27} \left (3+e^3\right ) \log ^2(2 x)-\frac {35 \left (8-e^3\right ) \log ^2(2 x)}{1296}+\frac {1}{54} \left (7-5 e^3\right ) \log ^2(2 x)-\frac {5}{432} \left (8-7 e^3\right ) \log ^2(2 x)-\frac {1}{432} \left (8-21 e^3\right ) \log ^2(2 x)+\frac {1}{36} e^3 \left (6-5 e^3\right ) \log (1-x)+\frac {5}{36} e^6 \log (1-x)-\frac {1}{6} e^3 \log (1-x)-\frac {35}{648} e^3 \left (1-e^3\right ) \log (x)-\frac {5}{216} e^3 \left (5-8 e^3\right ) \log (x)-\frac {1}{216} e^3 \left (13-30 e^3\right ) \log (x)+\frac {1}{288} e^3 \left (12-49 e^3\right ) \log (x)+\frac {1}{648} e^3 \left (17-62 e^3\right ) \log (x)+\frac {1}{864} e^3 \left (32-97 e^3\right ) \log (x)-\frac {e^3 \left (12-49 e^3\right ) \log \left (x^4+x^3+x^2+x+2\right )}{1152}-\frac {49 e^6 \log \left (x^4+x^3+x^2+x+2\right )}{1152}+\frac {305}{192} e^6 \int \frac {1}{\left (x^4+x^3+x^2+x+2\right )^3}dx+\frac {341}{288} e^6 \int \frac {x}{\left (x^4+x^3+x^2+x+2\right )^3}dx+\frac {209}{576} e^6 \int \frac {x^2}{\left (x^4+x^3+x^2+x+2\right )^3}dx-\frac {121}{288} e^6 \int \frac {1}{\left (x^4+x^3+x^2+x+2\right )^2}dx-\frac {17}{54} e^6 \int \frac {x}{\left (x^4+x^3+x^2+x+2\right )^2}dx-\frac {181}{864} e^6 \int \frac {x^2}{\left (x^4+x^3+x^2+x+2\right )^2}dx+\frac {e^3 \left (756-95 e^3\right ) \int \frac {1}{x^4+x^3+x^2+x+2}dx}{3456}-\frac {337 e^6 \int \frac {1}{x^4+x^3+x^2+x+2}dx}{3456}+\frac {e^3 \left (684+287 e^3\right ) \int \frac {x}{x^4+x^3+x^2+x+2}dx}{1728}-\frac {239 e^6 \int \frac {x}{x^4+x^3+x^2+x+2}dx}{1728}+\frac {e^3 \left (252+515 e^3\right ) \int \frac {x^2}{x^4+x^3+x^2+x+2}dx}{3456}-\frac {379 e^6 \int \frac {x^2}{x^4+x^3+x^2+x+2}dx}{3456}+\frac {11}{12} e^3 \int \frac {\log (2 x)}{\left (x^4+x^3+x^2+x+2\right )^2}dx+\frac {13}{4} e^3 \int \frac {x \log (2 x)}{\left (x^4+x^3+x^2+x+2\right )^2}dx+\frac {19}{12} e^3 \int \frac {x^2 \log (2 x)}{\left (x^4+x^3+x^2+x+2\right )^2}dx+\frac {5}{12} e^3 \int \frac {x^3 \log (2 x)}{\left (x^4+x^3+x^2+x+2\right )^2}dx-\frac {1}{4} e^3 \int \frac {\log (2 x)}{x^4+x^3+x^2+x+2}dx-\frac {3}{4} e^3 \int \frac {x \log (2 x)}{x^4+x^3+x^2+x+2}dx-\frac {1}{12} e^3 \int \frac {x^2 \log (2 x)}{x^4+x^3+x^2+x+2}dx-\frac {11 e^6}{108 (1-x)}+\frac {83 e^6}{864 \left (x^4+x^3+x^2+x+2\right )}-\frac {e^6}{72 (1-x)^2}+\frac {119 e^6}{1152 \left (x^4+x^3+x^2+x+2\right )^2}-\frac {e^3 \log (2 x)}{4 x}+\frac {e^3 \left (58+23 e^3\right )}{216 x}+\frac {5 e^3 \left (4-7 e^3\right )}{216 x}-\frac {e^3 \left (15-11 e^3\right )}{162 x}+\frac {e^3 \left (4-11 e^3\right )}{108 x}-\frac {e^3 \left (24-35 e^3\right )}{432 x}-\frac {35 e^6}{648 x}-\frac {e^3}{4 x}-\frac {e^3 \log (2 x)}{2 x^2}-\frac {e^3 \left (56+11 e^3\right )}{864 x^2}+\frac {e^3 \left (24+11 e^3\right )}{432 x^2}+\frac {e^3 \left (31+8 e^3\right )}{324 x^2}+\frac {35 e^3 \left (4-e^3\right )}{1296 x^2}+\frac {5 e^3 \left (2-3 e^3\right )}{216 x^2}+\frac {e^3 \left (4-15 e^3\right )}{432 x^2}-\frac {e^3}{4 x^2}-\frac {e^6}{8 x^3}-\frac {e^6}{8 x^4}\right )\) |
Input:
Int[(E^6*(8 - 6*x) + E^3*(-8*x^2 + 8*x^3 - 2*x^4) + 2*x^19*Log[2*x] + (-16 *x^4 + 24*x^5 - 12*x^6 + 2*x^7 + E^3*(16*x^2 - 20*x^3 + 6*x^4))*Log[2*x] + x^10*(-2*E^3*x^2 + (14*E^3*x^2 - 12*x^4 + 6*x^5)*Log[2*x]) + x^5*(-14*E^6 + E^3*(8*x^2 - 4*x^3) + (24*x^4 - 24*x^5 + 6*x^6 + E^3*(-36*x^2 + 20*x^3) )*Log[2*x]))/(-8*x^5 + 12*x^6 - 6*x^7 + x^8 + x^20 + x^10*(-6*x^5 + 3*x^6) + x^5*(12*x^5 - 12*x^6 + 3*x^7)),x]
Output:
$Aborted
Time = 87.15 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.71
| method | result | size |
| risch | \(\ln \left (2 x \right )^{2}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2} \left (x^{5}+x -2\right )}+\frac {{\mathrm e}^{6}}{\left (x^{5}+x -2\right )^{2} x^{4}}\) | \(41\) |
| parallelrisch | \(\frac {{\mathrm e}^{6}-2 \ln \left (2 x \right ) {\mathrm e}^{3} x^{7}-2 \ln \left (2 x \right ) {\mathrm e}^{3} x^{3}+4 \ln \left (2 x \right ) {\mathrm e}^{3} x^{2}+\ln \left (2 x \right )^{2} x^{14}+2 \ln \left (2 x \right )^{2} x^{10}-4 \ln \left (2 x \right )^{2} x^{9}+\ln \left (2 x \right )^{2} x^{6}-4 \ln \left (2 x \right )^{2} x^{5}+4 \ln \left (2 x \right )^{2} x^{4}}{x^{4} \left (x^{10}+2 x^{6}-4 x^{5}+x^{2}-4 x +4\right )}\) | \(130\) |
| parts | \(\frac {{\mathrm e}^{3}}{2 x^{2}}+\frac {{\mathrm e}^{3} \ln \left (-2+2 x \right )}{3}+\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{4}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{3}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {12 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{2}}{16 x^{4}+16 x^{3}+16 x^{2}+16 x +32}-\frac {20 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}+\frac {{\mathrm e}^{3} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 \textit {\_Z}^{3}+4 \textit {\_Z}^{2}+8 \textit {\_Z} +32\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+2 \textit {\_R}^{2}+36 \textit {\_R} +40\right ) \ln \left (2 x -\textit {\_R} \right )}{2 \textit {\_R}^{3}+3 \textit {\_R}^{2}+4 \textit {\_R} +4}\right )}{24}+\frac {{\mathrm e}^{3}}{2 x}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{2 x}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2}}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (-2+2 x \right )}+\ln \left (2 x \right )^{2}-2 \,{\mathrm e}^{3} \left (\frac {-17 x^{7} {\mathrm e}^{3}-\frac {63 x^{6} {\mathrm e}^{3}}{2}-24 x^{5} {\mathrm e}^{3}+\frac {23 x^{4} {\mathrm e}^{3}}{2}-7 x^{3} {\mathrm e}^{3}+\frac {67 x^{2} {\mathrm e}^{3}}{2}+100 x \,{\mathrm e}^{3}+\frac {265 \,{\mathrm e}^{3}}{2}}{432 \left (x^{4}+x^{3}+x^{2}+x +2\right )^{2}}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+\textit {\_Z}^{3}+\textit {\_Z}^{2}+\textit {\_Z} +2\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+\textit {\_R}^{2}+9 \textit {\_R} +5\right ) \ln \left (x -\textit {\_R} \right )}{4 \textit {\_R}^{3}+3 \textit {\_R}^{2}+2 \textit {\_R} +1}\right )}{24}+\frac {\ln \left (-1+x \right )}{6}-\frac {{\mathrm e}^{3}}{72 \left (-1+x \right )^{2}}+\frac {11 \,{\mathrm e}^{3}}{108 \left (-1+x \right )}-\frac {\ln \left (x \right )}{8}-\frac {\frac {{\mathrm e}^{3}}{16}-\frac {1}{4}}{x}-\frac {\frac {3 \,{\mathrm e}^{3}}{16}-\frac {1}{2}}{2 x^{2}}-\frac {{\mathrm e}^{3}}{8 x^{4}}-\frac {{\mathrm e}^{3}}{8 x^{3}}\right )\) | \(458\) |
| derivativedivides | \(\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{4}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{3}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {12 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{2}}{16 x^{4}+16 x^{3}+16 x^{2}+16 x +32}-\frac {20 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (-2+2 x \right )}+\frac {{\mathrm e}^{3}}{2 x^{2}}+\frac {{\mathrm e}^{3} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 \textit {\_Z}^{3}+4 \textit {\_Z}^{2}+8 \textit {\_Z} +32\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+2 \textit {\_R}^{2}+36 \textit {\_R} +40\right ) \ln \left (2 x -\textit {\_R} \right )}{2 \textit {\_R}^{3}+3 \textit {\_R}^{2}+4 \textit {\_R} +4}\right )}{24}+\frac {{\mathrm e}^{3}}{2 x}+\frac {{\mathrm e}^{3} \ln \left (-2+2 x \right )}{3}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{2 x}+\ln \left (2 x \right )^{2}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2}}-256 \,{\mathrm e}^{3} \left (-\frac {\ln \left (2 x \right )}{1024}-\frac {\frac {{\mathrm e}^{3}}{1024}-\frac {1}{256}}{2 x}-\frac {\frac {3 \,{\mathrm e}^{3}}{512}-\frac {1}{64}}{8 x^{2}}-\frac {{\mathrm e}^{3}}{1024 x^{4}}-\frac {{\mathrm e}^{3}}{1024 x^{3}}+\frac {\ln \left (-2+2 x \right )}{768}-\frac {{\mathrm e}^{3}}{2304 \left (-2+2 x \right )^{2}}+\frac {11 \,{\mathrm e}^{3}}{6912 \left (-2+2 x \right )}+\frac {-2176 x^{7} {\mathrm e}^{3}-4032 x^{6} {\mathrm e}^{3}-3072 x^{5} {\mathrm e}^{3}+1472 x^{4} {\mathrm e}^{3}-896 x^{3} {\mathrm e}^{3}+4288 x^{2} {\mathrm e}^{3}+12800 x \,{\mathrm e}^{3}+16960 \,{\mathrm e}^{3}}{27648 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 \textit {\_Z}^{3}+4 \textit {\_Z}^{2}+8 \textit {\_Z} +32\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+2 \textit {\_R}^{2}+36 \textit {\_R} +40\right ) \ln \left (2 x -\textit {\_R} \right )}{2 \textit {\_R}^{3}+3 \textit {\_R}^{2}+4 \textit {\_R} +4}\right )}{6144}\right )\) | \(484\) |
| default | \(\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{4}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {4 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{3}}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {12 \,{\mathrm e}^{3} \ln \left (2 x \right ) x^{2}}{16 x^{4}+16 x^{3}+16 x^{2}+16 x +32}-\frac {20 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )}-\frac {2 \,{\mathrm e}^{3} \ln \left (2 x \right ) x}{3 \left (-2+2 x \right )}+\frac {{\mathrm e}^{3}}{2 x^{2}}+\frac {{\mathrm e}^{3} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 \textit {\_Z}^{3}+4 \textit {\_Z}^{2}+8 \textit {\_Z} +32\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+2 \textit {\_R}^{2}+36 \textit {\_R} +40\right ) \ln \left (2 x -\textit {\_R} \right )}{2 \textit {\_R}^{3}+3 \textit {\_R}^{2}+4 \textit {\_R} +4}\right )}{24}+\frac {{\mathrm e}^{3}}{2 x}+\frac {{\mathrm e}^{3} \ln \left (-2+2 x \right )}{3}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{2 x}+\ln \left (2 x \right )^{2}+\frac {{\mathrm e}^{3} \ln \left (2 x \right )}{x^{2}}-256 \,{\mathrm e}^{3} \left (-\frac {\ln \left (2 x \right )}{1024}-\frac {\frac {{\mathrm e}^{3}}{1024}-\frac {1}{256}}{2 x}-\frac {\frac {3 \,{\mathrm e}^{3}}{512}-\frac {1}{64}}{8 x^{2}}-\frac {{\mathrm e}^{3}}{1024 x^{4}}-\frac {{\mathrm e}^{3}}{1024 x^{3}}+\frac {\ln \left (-2+2 x \right )}{768}-\frac {{\mathrm e}^{3}}{2304 \left (-2+2 x \right )^{2}}+\frac {11 \,{\mathrm e}^{3}}{6912 \left (-2+2 x \right )}+\frac {-2176 x^{7} {\mathrm e}^{3}-4032 x^{6} {\mathrm e}^{3}-3072 x^{5} {\mathrm e}^{3}+1472 x^{4} {\mathrm e}^{3}-896 x^{3} {\mathrm e}^{3}+4288 x^{2} {\mathrm e}^{3}+12800 x \,{\mathrm e}^{3}+16960 \,{\mathrm e}^{3}}{27648 \left (16 x^{4}+16 x^{3}+16 x^{2}+16 x +32\right )^{2}}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 \textit {\_Z}^{3}+4 \textit {\_Z}^{2}+8 \textit {\_Z} +32\right )}{\sum }\frac {\left (-\textit {\_R}^{3}+2 \textit {\_R}^{2}+36 \textit {\_R} +40\right ) \ln \left (2 x -\textit {\_R} \right )}{2 \textit {\_R}^{3}+3 \textit {\_R}^{2}+4 \textit {\_R} +4}\right )}{6144}\right )\) | \(484\) |
Input:
int((2*x^19*ln(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*ln(2*x)-2*x^2*exp(3))*x^ 10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24*x^5+24*x^4)*ln(2*x)-14*exp(3)^2+(-4*x ^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+24*x^5-16 *x^4)*ln(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3*x^6- 6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x,method=_RE TURNVERBOSE)
Output:
ln(2*x)^2-2*exp(3)/x^2/(x^5+x-2)*ln(2*x)+exp(6)/(x^5+x-2)^2/x^4
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 91, normalized size of antiderivative = 3.79 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=-\frac {2 \, {\left (x^{7} + x^{3} - 2 \, x^{2}\right )} e^{3} \log \left (2 \, x\right ) - {\left (x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (2 \, x\right )^{2} - e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \] Input:
integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*ex p(3))*x^10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3 )^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+ 24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^ 20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="fricas")
Output:
-(2*(x^7 + x^3 - 2*x^2)*e^3*log(2*x) - (x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^ 5 + 4*x^4)*log(2*x)^2 - e^6)/(x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (19) = 38\).
Time = 0.61 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.42 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\log {\left (2 x \right )}^{2} + \frac {e^{6}}{x^{14} + 2 x^{10} - 4 x^{9} + x^{6} - 4 x^{5} + 4 x^{4}} - \frac {2 e^{3} \log {\left (2 x \right )}}{x^{7} + x^{3} - 2 x^{2}} \] Input:
integrate((2*x**19*ln(2*x)+((14*x**2*exp(3)+6*x**5-12*x**4)*ln(2*x)-2*x**2 *exp(3))*x**10+(((20*x**3-36*x**2)*exp(3)+6*x**6-24*x**5+24*x**4)*ln(2*x)- 14*exp(3)**2+(-4*x**3+8*x**2)*exp(3))*x**5+((6*x**4-20*x**3+16*x**2)*exp(3 )+2*x**7-12*x**6+24*x**5-16*x**4)*ln(2*x)+(-6*x+8)*exp(3)**2+(-2*x**4+8*x* *3-8*x**2)*exp(3))/(x**20+(3*x**6-6*x**5)*x**10+(3*x**7-12*x**6+12*x**5)*x **5+x**8-6*x**7+12*x**6-8*x**5),x)
Output:
log(2*x)**2 + exp(6)/(x**14 + 2*x**10 - 4*x**9 + x**6 - 4*x**5 + 4*x**4) - 2*exp(3)*log(2*x)/(x**7 + x**3 - 2*x**2)
Leaf count of result is larger than twice the leaf count of optimal. 162 vs. \(2 (23) = 46\).
Time = 0.16 (sec) , antiderivative size = 162, normalized size of antiderivative = 6.75 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=-\frac {2 \, x^{7} e^{3} \log \left (2\right ) + 2 \, x^{3} e^{3} \log \left (2\right ) - 4 \, x^{2} e^{3} \log \left (2\right ) - {\left (x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (x\right )^{2} - 2 \, {\left (x^{14} \log \left (2\right ) + 2 \, x^{10} \log \left (2\right ) - 4 \, x^{9} \log \left (2\right ) - x^{7} e^{3} + x^{6} \log \left (2\right ) - 4 \, x^{5} \log \left (2\right ) + 4 \, x^{4} \log \left (2\right ) - x^{3} e^{3} + 2 \, x^{2} e^{3}\right )} \log \left (x\right ) - e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \] Input:
integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*ex p(3))*x^10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3 )^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+ 24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^ 20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="maxima")
Output:
-(2*x^7*e^3*log(2) + 2*x^3*e^3*log(2) - 4*x^2*e^3*log(2) - (x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4)*log(x)^2 - 2*(x^14*log(2) + 2*x^10*log(2) - 4*x^9*log(2) - x^7*e^3 + x^6*log(2) - 4*x^5*log(2) + 4*x^4*log(2) - x^3*e ^3 + 2*x^2*e^3)*log(x) - e^6)/(x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4*x^4 )
Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (23) = 46\).
Time = 0.15 (sec) , antiderivative size = 130, normalized size of antiderivative = 5.42 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\frac {x^{14} \log \left (2 \, x\right )^{2} + 2 \, x^{10} \log \left (2 \, x\right )^{2} - 4 \, x^{9} \log \left (2 \, x\right )^{2} - 2 \, x^{7} e^{3} \log \left (2 \, x\right ) + x^{6} \log \left (2 \, x\right )^{2} - 4 \, x^{5} \log \left (2 \, x\right )^{2} + 4 \, x^{4} \log \left (2 \, x\right )^{2} - 2 \, x^{3} e^{3} \log \left (2 \, x\right ) + 4 \, x^{2} e^{3} \log \left (2 \, x\right ) + e^{6}}{x^{14} + 2 \, x^{10} - 4 \, x^{9} + x^{6} - 4 \, x^{5} + 4 \, x^{4}} \] Input:
integrate((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*ex p(3))*x^10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3 )^2+(-4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+ 24*x^5-16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^ 20+(3*x^6-6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x, algorithm="giac")
Output:
(x^14*log(2*x)^2 + 2*x^10*log(2*x)^2 - 4*x^9*log(2*x)^2 - 2*x^7*e^3*log(2* x) + x^6*log(2*x)^2 - 4*x^5*log(2*x)^2 + 4*x^4*log(2*x)^2 - 2*x^3*e^3*log( 2*x) + 4*x^2*e^3*log(2*x) + e^6)/(x^14 + 2*x^10 - 4*x^9 + x^6 - 4*x^5 + 4* x^4)
Time = 3.76 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.83 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\frac {{\left ({\mathrm {e}}^3+2\,x^2\,\ln \left (2\,x\right )-x^3\,\ln \left (2\,x\right )-x^7\,\ln \left (2\,x\right )\right )}^2}{x^4\,{\left (x^5+x-2\right )}^2} \] Input:
int(-(x^5*(14*exp(6) + log(2*x)*(exp(3)*(36*x^2 - 20*x^3) - 24*x^4 + 24*x^ 5 - 6*x^6) - exp(3)*(8*x^2 - 4*x^3)) - x^10*(log(2*x)*(14*x^2*exp(3) - 12* x^4 + 6*x^5) - 2*x^2*exp(3)) - 2*x^19*log(2*x) - log(2*x)*(exp(3)*(16*x^2 - 20*x^3 + 6*x^4) - 16*x^4 + 24*x^5 - 12*x^6 + 2*x^7) + exp(3)*(8*x^2 - 8* x^3 + 2*x^4) + exp(6)*(6*x - 8))/(x^5*(12*x^5 - 12*x^6 + 3*x^7) - x^10*(6* x^5 - 3*x^6) - 8*x^5 + 12*x^6 - 6*x^7 + x^8 + x^20),x)
Output:
(exp(3) + 2*x^2*log(2*x) - x^3*log(2*x) - x^7*log(2*x))^2/(x^4*(x + x^5 - 2)^2)
Time = 0.19 (sec) , antiderivative size = 131, normalized size of antiderivative = 5.46 \[ \int \frac {e^6 (8-6 x)+e^3 \left (-8 x^2+8 x^3-2 x^4\right )+2 x^{19} \log (2 x)+\left (-16 x^4+24 x^5-12 x^6+2 x^7+e^3 \left (16 x^2-20 x^3+6 x^4\right )\right ) \log (2 x)+x^{10} \left (-2 e^3 x^2+\left (14 e^3 x^2-12 x^4+6 x^5\right ) \log (2 x)\right )+x^5 \left (-14 e^6+e^3 \left (8 x^2-4 x^3\right )+\left (24 x^4-24 x^5+6 x^6+e^3 \left (-36 x^2+20 x^3\right )\right ) \log (2 x)\right )}{-8 x^5+12 x^6-6 x^7+x^8+x^{20}+x^{10} \left (-6 x^5+3 x^6\right )+x^5 \left (12 x^5-12 x^6+3 x^7\right )} \, dx=\frac {\mathrm {log}\left (2 x \right )^{2} x^{14}+2 \mathrm {log}\left (2 x \right )^{2} x^{10}-4 \mathrm {log}\left (2 x \right )^{2} x^{9}+\mathrm {log}\left (2 x \right )^{2} x^{6}-4 \mathrm {log}\left (2 x \right )^{2} x^{5}+4 \mathrm {log}\left (2 x \right )^{2} x^{4}-2 \,\mathrm {log}\left (2 x \right ) e^{3} x^{7}-2 \,\mathrm {log}\left (2 x \right ) e^{3} x^{3}+4 \,\mathrm {log}\left (2 x \right ) e^{3} x^{2}+e^{6}}{x^{4} \left (x^{10}+2 x^{6}-4 x^{5}+x^{2}-4 x +4\right )} \] Input:
int((2*x^19*log(2*x)+((14*x^2*exp(3)+6*x^5-12*x^4)*log(2*x)-2*x^2*exp(3))* x^10+(((20*x^3-36*x^2)*exp(3)+6*x^6-24*x^5+24*x^4)*log(2*x)-14*exp(3)^2+(- 4*x^3+8*x^2)*exp(3))*x^5+((6*x^4-20*x^3+16*x^2)*exp(3)+2*x^7-12*x^6+24*x^5 -16*x^4)*log(2*x)+(-6*x+8)*exp(3)^2+(-2*x^4+8*x^3-8*x^2)*exp(3))/(x^20+(3* x^6-6*x^5)*x^10+(3*x^7-12*x^6+12*x^5)*x^5+x^8-6*x^7+12*x^6-8*x^5),x)
Output:
(log(2*x)**2*x**14 + 2*log(2*x)**2*x**10 - 4*log(2*x)**2*x**9 + log(2*x)** 2*x**6 - 4*log(2*x)**2*x**5 + 4*log(2*x)**2*x**4 - 2*log(2*x)*e**3*x**7 - 2*log(2*x)*e**3*x**3 + 4*log(2*x)*e**3*x**2 + e**6)/(x**4*(x**10 + 2*x**6 - 4*x**5 + x**2 - 4*x + 4))