Integrand size = 241, antiderivative size = 22 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \] Output:
(4+x)^2*x^12*(ln(x*ln(3*x)^2)+x)^4
Time = 5.06 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \] Input:
Integrate[(128*x^14 + 64*x^15 + 8*x^16 + (64*x^14 + 288*x^15 + 140*x^16 + 18*x^17)*Log[3*x] + (384*x^13 + 192*x^14 + 24*x^15 + (192*x^13 + 1056*x^14 + 524*x^15 + 68*x^16)*Log[3*x])*Log[x*Log[3*x]^2] + (384*x^12 + 192*x^13 + 24*x^14 + (192*x^12 + 1440*x^13 + 732*x^14 + 96*x^15)*Log[3*x])*Log[x*Lo g[3*x]^2]^2 + (128*x^11 + 64*x^12 + 8*x^13 + (64*x^11 + 864*x^12 + 452*x^1 3 + 60*x^14)*Log[3*x])*Log[x*Log[3*x]^2]^3 + (192*x^11 + 104*x^12 + 14*x^1 3)*Log[3*x]*Log[x*Log[3*x]^2]^4)/Log[3*x],x]
Output:
x^12*(4 + x)^2*(x + Log[x*Log[3*x]^2])^4
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.
| \(\displaystyle \int \frac {8 x^{16}+64 x^{15}+128 x^{14}+\left (14 x^{13}+104 x^{12}+192 x^{11}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )+\left (18 x^{17}+140 x^{16}+288 x^{15}+64 x^{14}\right ) \log (3 x)+\left (24 x^{15}+192 x^{14}+384 x^{13}+\left (68 x^{16}+524 x^{15}+1056 x^{14}+192 x^{13}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (24 x^{14}+192 x^{13}+384 x^{12}+\left (96 x^{15}+732 x^{14}+1440 x^{13}+192 x^{12}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (8 x^{13}+64 x^{12}+128 x^{11}+\left (60 x^{14}+452 x^{13}+864 x^{12}+64 x^{11}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )+4 (x+4)\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {(x+4) \left (9 \log (3 x) x^2+34 \log (3 x) x+4 x+8 \log (3 x)+16\right ) x^{14}}{\log (3 x)}+\frac {2 (x+4) \left (17 \log (3 x) x^2+63 \log (3 x) x+6 x+12 \log (3 x)+24\right ) \log \left (x \log ^2(3 x)\right ) x^{13}}{\log (3 x)}+\frac {6 (x+4) \left (8 \log (3 x) x^2+29 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^2\left (x \log ^2(3 x)\right ) x^{12}}{\log (3 x)}+(x+4) (7 x+24) \log ^4\left (x \log ^2(3 x)\right ) x^{11}+\frac {2 (x+4) \left (15 \log (3 x) x^2+53 \log (3 x) x+2 x+4 \log (3 x)+8\right ) \log ^3\left (x \log ^2(3 x)\right ) x^{11}}{\log (3 x)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x^{11} (x+4) \left (x+\log \left (x \log ^2(3 x)\right )\right )^3 \left (4 (x+4)+\log (3 x) \left (9 x^2+34 x+(7 x+24) \log \left (x \log ^2(3 x)\right )+8\right )\right )}{\log (3 x)}dx\) |
Input:
Int[(128*x^14 + 64*x^15 + 8*x^16 + (64*x^14 + 288*x^15 + 140*x^16 + 18*x^1 7)*Log[3*x] + (384*x^13 + 192*x^14 + 24*x^15 + (192*x^13 + 1056*x^14 + 524 *x^15 + 68*x^16)*Log[3*x])*Log[x*Log[3*x]^2] + (384*x^12 + 192*x^13 + 24*x ^14 + (192*x^12 + 1440*x^13 + 732*x^14 + 96*x^15)*Log[3*x])*Log[x*Log[3*x] ^2]^2 + (128*x^11 + 64*x^12 + 8*x^13 + (64*x^11 + 864*x^12 + 452*x^13 + 60 *x^14)*Log[3*x])*Log[x*Log[3*x]^2]^3 + (192*x^11 + 104*x^12 + 14*x^13)*Log [3*x]*Log[x*Log[3*x]^2]^4)/Log[3*x],x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(199\) vs. \(2(22)=44\).
Time = 4.14 (sec) , antiderivative size = 200, normalized size of antiderivative = 9.09
| method | result | size |
| parallelrisch | \(x^{18}+4 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{17}+6 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{16}+4 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{15}+\ln \left (x \ln \left (3 x \right )^{2}\right )^{4} x^{14}+8 x^{17}+32 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{16}+48 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{15}+32 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{14}+8 \ln \left (x \ln \left (3 x \right )^{2}\right )^{4} x^{13}+16 x^{16}+64 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{15}+96 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{14}+64 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{13}+16 \ln \left (x \ln \left (3 x \right )^{2}\right )^{4} x^{12}\) | \(200\) |
Input:
int(((14*x^13+104*x^12+192*x^11)*ln(3*x)*ln(x*ln(3*x)^2)^4+((60*x^14+452*x ^13+864*x^12+64*x^11)*ln(3*x)+8*x^13+64*x^12+128*x^11)*ln(x*ln(3*x)^2)^3+( (96*x^15+732*x^14+1440*x^13+192*x^12)*ln(3*x)+24*x^14+192*x^13+384*x^12)*l n(x*ln(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*ln(3*x)+24*x^15+19 2*x^14+384*x^13)*ln(x*ln(3*x)^2)+(18*x^17+140*x^16+288*x^15+64*x^14)*ln(3* x)+8*x^16+64*x^15+128*x^14)/ln(3*x),x,method=_RETURNVERBOSE)
Output:
x^18+4*ln(x*ln(3*x)^2)*x^17+6*ln(x*ln(3*x)^2)^2*x^16+4*ln(x*ln(3*x)^2)^3*x ^15+ln(x*ln(3*x)^2)^4*x^14+8*x^17+32*ln(x*ln(3*x)^2)*x^16+48*ln(x*ln(3*x)^ 2)^2*x^15+32*ln(x*ln(3*x)^2)^3*x^14+8*ln(x*ln(3*x)^2)^4*x^13+16*x^16+64*ln (x*ln(3*x)^2)*x^15+96*ln(x*ln(3*x)^2)^2*x^14+64*ln(x*ln(3*x)^2)^3*x^13+16* ln(x*ln(3*x)^2)^4*x^12
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (22) = 44\).
Time = 0.10 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.41 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{18} + 8 \, x^{17} + 16 \, x^{16} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} + 4 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 4 \, {\left (x^{17} + 8 \, x^{16} + 16 \, x^{15}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) \] Input:
integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x ^14+452*x^13+864*x^12+64*x^11)*log(3*x)+8*x^13+64*x^12+128*x^11)*log(x*log (3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x^1 3+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log (3*x)+24*x^15+192*x^14+384*x^13)*log(x*log(3*x)^2)+(18*x^17+140*x^16+288*x ^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="fric as")
Output:
x^18 + 8*x^17 + 16*x^16 + (x^14 + 8*x^13 + 16*x^12)*log(x*log(3*x)^2)^4 + 4*(x^15 + 8*x^14 + 16*x^13)*log(x*log(3*x)^2)^3 + 6*(x^16 + 8*x^15 + 16*x^ 14)*log(x*log(3*x)^2)^2 + 4*(x^17 + 8*x^16 + 16*x^15)*log(x*log(3*x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (20) = 40\).
Time = 0.43 (sec) , antiderivative size = 117, normalized size of antiderivative = 5.32 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{18} + 8 x^{17} + 16 x^{16} + \left (x^{14} + 8 x^{13} + 16 x^{12}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{4} + \left (4 x^{15} + 32 x^{14} + 64 x^{13}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{3} + \left (6 x^{16} + 48 x^{15} + 96 x^{14}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{2} + \left (4 x^{17} + 32 x^{16} + 64 x^{15}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )} \] Input:
integrate(((14*x**13+104*x**12+192*x**11)*ln(3*x)*ln(x*ln(3*x)**2)**4+((60 *x**14+452*x**13+864*x**12+64*x**11)*ln(3*x)+8*x**13+64*x**12+128*x**11)*l n(x*ln(3*x)**2)**3+((96*x**15+732*x**14+1440*x**13+192*x**12)*ln(3*x)+24*x **14+192*x**13+384*x**12)*ln(x*ln(3*x)**2)**2+((68*x**16+524*x**15+1056*x* *14+192*x**13)*ln(3*x)+24*x**15+192*x**14+384*x**13)*ln(x*ln(3*x)**2)+(18* x**17+140*x**16+288*x**15+64*x**14)*ln(3*x)+8*x**16+64*x**15+128*x**14)/ln (3*x),x)
Output:
x**18 + 8*x**17 + 16*x**16 + (x**14 + 8*x**13 + 16*x**12)*log(x*log(3*x)** 2)**4 + (4*x**15 + 32*x**14 + 64*x**13)*log(x*log(3*x)**2)**3 + (6*x**16 + 48*x**15 + 96*x**14)*log(x*log(3*x)**2)**2 + (4*x**17 + 32*x**16 + 64*x** 15)*log(x*log(3*x)**2)
\[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\int { \frac {2 \, {\left (4 \, x^{16} + 32 \, x^{15} + 64 \, x^{14} + {\left (7 \, x^{13} + 52 \, x^{12} + 96 \, x^{11}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} \log \left (3 \, x\right ) + 2 \, {\left (2 \, x^{13} + 16 \, x^{12} + 32 \, x^{11} + {\left (15 \, x^{14} + 113 \, x^{13} + 216 \, x^{12} + 16 \, x^{11}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (2 \, x^{14} + 16 \, x^{13} + 32 \, x^{12} + {\left (8 \, x^{15} + 61 \, x^{14} + 120 \, x^{13} + 16 \, x^{12}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 2 \, {\left (6 \, x^{15} + 48 \, x^{14} + 96 \, x^{13} + {\left (17 \, x^{16} + 131 \, x^{15} + 264 \, x^{14} + 48 \, x^{13}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) + {\left (9 \, x^{17} + 70 \, x^{16} + 144 \, x^{15} + 32 \, x^{14}\right )} \log \left (3 \, x\right )\right )}}{\log \left (3 \, x\right )} \,d x } \] Input:
integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x ^14+452*x^13+864*x^12+64*x^11)*log(3*x)+8*x^13+64*x^12+128*x^11)*log(x*log (3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x^1 3+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log (3*x)+24*x^15+192*x^14+384*x^13)*log(x*log(3*x)^2)+(18*x^17+140*x^16+288*x ^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="maxi ma")
Output:
x^18 + 8*x^17 + 16*x^16 + (x^14 + 8*x^13 + 16*x^12)*log(x)^4 + 16*(x^14 + 8*x^13 + 16*x^12)*log(log(3) + log(x))^4 + 4*(x^15 + 8*x^14 + 16*x^13)*log (x)^3 + 32*(x^15 + 8*x^14 + 16*x^13 + (x^14 + 8*x^13 + 16*x^12)*log(x))*lo g(log(3) + log(x))^3 + 6*(x^16 + 8*x^15 + 16*x^14)*log(x)^2 + 24*(x^16 + 8 *x^15 + 16*x^14 + (x^14 + 8*x^13 + 16*x^12)*log(x)^2 + 2*(x^15 + 8*x^14 + 16*x^13)*log(x))*log(log(3) + log(x))^2 + 4*(x^17 + 8*x^16 + 16*x^15)*log( x) + 8*(x^17 + 8*x^16 + 16*x^15 + (x^14 + 8*x^13 + 16*x^12)*log(x)^3 + 3*( x^15 + 8*x^14 + 16*x^13)*log(x)^2 + 3*(x^16 + 8*x^15 + 16*x^14)*log(x))*lo g(log(3) + log(x)) + 8/129140163*Ei(17*log(3*x)) + 64/43046721*Ei(16*log(3 *x)) + 128/14348907*Ei(15*log(3*x)) - 2*integrate(4*(x^16 + 8*x^15 + 16*x^ 14)/(log(3) + log(x)), x)
\[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\int { \frac {2 \, {\left (4 \, x^{16} + 32 \, x^{15} + 64 \, x^{14} + {\left (7 \, x^{13} + 52 \, x^{12} + 96 \, x^{11}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} \log \left (3 \, x\right ) + 2 \, {\left (2 \, x^{13} + 16 \, x^{12} + 32 \, x^{11} + {\left (15 \, x^{14} + 113 \, x^{13} + 216 \, x^{12} + 16 \, x^{11}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (2 \, x^{14} + 16 \, x^{13} + 32 \, x^{12} + {\left (8 \, x^{15} + 61 \, x^{14} + 120 \, x^{13} + 16 \, x^{12}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 2 \, {\left (6 \, x^{15} + 48 \, x^{14} + 96 \, x^{13} + {\left (17 \, x^{16} + 131 \, x^{15} + 264 \, x^{14} + 48 \, x^{13}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) + {\left (9 \, x^{17} + 70 \, x^{16} + 144 \, x^{15} + 32 \, x^{14}\right )} \log \left (3 \, x\right )\right )}}{\log \left (3 \, x\right )} \,d x } \] Input:
integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x ^14+452*x^13+864*x^12+64*x^11)*log(3*x)+8*x^13+64*x^12+128*x^11)*log(x*log (3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x^1 3+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log (3*x)+24*x^15+192*x^14+384*x^13)*log(x*log(3*x)^2)+(18*x^17+140*x^16+288*x ^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="giac ")
Output:
integrate(2*(4*x^16 + 32*x^15 + 64*x^14 + (7*x^13 + 52*x^12 + 96*x^11)*log (x*log(3*x)^2)^4*log(3*x) + 2*(2*x^13 + 16*x^12 + 32*x^11 + (15*x^14 + 113 *x^13 + 216*x^12 + 16*x^11)*log(3*x))*log(x*log(3*x)^2)^3 + 6*(2*x^14 + 16 *x^13 + 32*x^12 + (8*x^15 + 61*x^14 + 120*x^13 + 16*x^12)*log(3*x))*log(x* log(3*x)^2)^2 + 2*(6*x^15 + 48*x^14 + 96*x^13 + (17*x^16 + 131*x^15 + 264* x^14 + 48*x^13)*log(3*x))*log(x*log(3*x)^2) + (9*x^17 + 70*x^16 + 144*x^15 + 32*x^14)*log(3*x))/log(3*x), x)
Time = 4.18 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.55 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\ln \left (x\,{\ln \left (3\,x\right )}^2\right )\,\left (4\,x^{17}+32\,x^{16}+64\,x^{15}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^4\,\left (x^{14}+8\,x^{13}+16\,x^{12}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^3\,\left (4\,x^{15}+32\,x^{14}+64\,x^{13}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^2\,\left (6\,x^{16}+48\,x^{15}+96\,x^{14}\right )+16\,x^{16}+8\,x^{17}+x^{18} \] Input:
int((log(x*log(3*x)^2)*(384*x^13 + 192*x^14 + 24*x^15 + log(3*x)*(192*x^13 + 1056*x^14 + 524*x^15 + 68*x^16)) + log(x*log(3*x)^2)^3*(128*x^11 + 64*x ^12 + 8*x^13 + log(3*x)*(64*x^11 + 864*x^12 + 452*x^13 + 60*x^14)) + log(x *log(3*x)^2)^2*(384*x^12 + 192*x^13 + 24*x^14 + log(3*x)*(192*x^12 + 1440* x^13 + 732*x^14 + 96*x^15)) + 128*x^14 + 64*x^15 + 8*x^16 + log(3*x)*(64*x ^14 + 288*x^15 + 140*x^16 + 18*x^17) + log(3*x)*log(x*log(3*x)^2)^4*(192*x ^11 + 104*x^12 + 14*x^13))/log(3*x),x)
Output:
log(x*log(3*x)^2)*(64*x^15 + 32*x^16 + 4*x^17) + log(x*log(3*x)^2)^4*(16*x ^12 + 8*x^13 + x^14) + log(x*log(3*x)^2)^3*(64*x^13 + 32*x^14 + 4*x^15) + log(x*log(3*x)^2)^2*(96*x^14 + 48*x^15 + 6*x^16) + 16*x^16 + 8*x^17 + x^18
Time = 0.18 (sec) , antiderivative size = 196, normalized size of antiderivative = 8.91 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{12} \left (\mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{4} x^{2}+8 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{4} x +16 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{4}+4 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{3} x^{3}+32 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{3} x^{2}+64 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{3} x +6 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{2} x^{4}+48 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{2} x^{3}+96 \mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right )^{2} x^{2}+4 \,\mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right ) x^{5}+32 \,\mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right ) x^{4}+64 \,\mathrm {log}\left (\mathrm {log}\left (3 x \right )^{2} x \right ) x^{3}+x^{6}+8 x^{5}+16 x^{4}\right ) \] Input:
int(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x^14+45 2*x^13+864*x^12+64*x^11)*log(3*x)+8*x^13+64*x^12+128*x^11)*log(x*log(3*x)^ 2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x^13+384* x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log(3*x)+ 24*x^15+192*x^14+384*x^13)*log(x*log(3*x)^2)+(18*x^17+140*x^16+288*x^15+64 *x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x)
Output:
x**12*(log(log(3*x)**2*x)**4*x**2 + 8*log(log(3*x)**2*x)**4*x + 16*log(log (3*x)**2*x)**4 + 4*log(log(3*x)**2*x)**3*x**3 + 32*log(log(3*x)**2*x)**3*x **2 + 64*log(log(3*x)**2*x)**3*x + 6*log(log(3*x)**2*x)**2*x**4 + 48*log(l og(3*x)**2*x)**2*x**3 + 96*log(log(3*x)**2*x)**2*x**2 + 4*log(log(3*x)**2* x)*x**5 + 32*log(log(3*x)**2*x)*x**4 + 64*log(log(3*x)**2*x)*x**3 + x**6 + 8*x**5 + 16*x**4)