Integrand size = 137, antiderivative size = 30 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=4-\log ^2\left (\frac {\log (3+x)}{\left (x-\frac {9}{64} x \left (-x+x^2\right )^2\right )^2}\right ) \]
Time = 0.07 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=-\log ^2\left (\frac {4096 \log (3+x)}{x^2 \left (64-9 x^2+18 x^3-9 x^4\right )^2}\right ) \]
Integrate[((128*x - 18*x^3 + 36*x^4 - 18*x^5 + (-768 - 256*x + 324*x^2 - 7 56*x^3 + 252*x^4 + 180*x^5)*Log[3 + x])*Log[(4096*Log[3 + x])/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10)])/ ((-192*x - 64*x^2 + 27*x^3 - 45*x^4 + 9*x^5 + 9*x^6)*Log[3 + x]),x]
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.
| \(\displaystyle \int \frac {\left (-18 x^5+36 x^4-18 x^3+\left (180 x^5+252 x^4-756 x^3+324 x^2-256 x-768\right ) \log (x+3)+128 x\right ) \log \left (\frac {4096 \log (x+3)}{81 x^{10}-324 x^9+486 x^8-324 x^7-1071 x^6+2304 x^5-1152 x^4+4096 x^2}\right )}{\left (9 x^6+9 x^5-45 x^4+27 x^3-64 x^2-192 x\right ) \log (x+3)} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (-18 x^5+36 x^4-18 x^3+\left (180 x^5+252 x^4-756 x^3+324 x^2-256 x-768\right ) \log (x+3)+128 x\right ) \log \left (\frac {4096 \log (x+3)}{81 x^{10}-324 x^9+486 x^8-324 x^7-1071 x^6+2304 x^5-1152 x^4+4096 x^2}\right )}{x \left (9 x^5+9 x^4-45 x^3+27 x^2-64 x-192\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (-18 x^5+36 x^4-18 x^3+\left (180 x^5+252 x^4-756 x^3+324 x^2-256 x-768\right ) \log (x+3)+128 x\right ) \log \left (\frac {4096 \log (x+3)}{81 x^{10}-324 x^9+486 x^8-324 x^7-1071 x^6+2304 x^5-1152 x^4+4096 x^2}\right )}{1232 x (x+3) \log (x+3)}-\frac {3 (x-4) \left (-18 x^5+36 x^4-18 x^3+\left (180 x^5+252 x^4-756 x^3+324 x^2-256 x-768\right ) \log (x+3)+128 x\right ) \log \left (\frac {4096 \log (x+3)}{81 x^{10}-324 x^9+486 x^8-324 x^7-1071 x^6+2304 x^5-1152 x^4+4096 x^2}\right )}{448 x \left (3 x^2-3 x-8\right ) \log (x+3)}+\frac {3 (x-4) \left (-18 x^5+36 x^4-18 x^3+\left (180 x^5+252 x^4-756 x^3+324 x^2-256 x-768\right ) \log (x+3)+128 x\right ) \log \left (\frac {4096 \log (x+3)}{81 x^{10}-324 x^9+486 x^8-324 x^7-1071 x^6+2304 x^5-1152 x^4+4096 x^2}\right )}{704 x \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (9 x^5-18 x^4+9 x^3-2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)-64 x\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (-9 x^5+18 x^4-9 x^3+64 x-2 \left (-45 x^5-63 x^4+189 x^3-81 x^2+64 x+192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x-2 \left (-45 x^5-63 x^4+189 x^3-81 x^2+64 x+192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-9 x^5+18 x^4-9 x^3+64 x+2 \left (45 x^5+63 x^4-189 x^3+81 x^2-64 x-192\right ) \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{x (x+3) \left (-3 x^2+3 x+8\right ) \left (3 x^2-3 x+8\right ) \log (x+3)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{192 x \log (x+3)}+\frac {\left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{3696 (x+3) \log (x+3)}-\frac {3 (3 x-5) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{896 \left (3 x^2-3 x-8\right ) \log (x+3)}-\frac {3 (3 x-1) \left (90 \log (x+3) x^5-9 x^5+126 \log (x+3) x^4+18 x^4-378 \log (x+3) x^3-9 x^3+162 \log (x+3) x^2-128 \log (x+3) x+64 x-384 \log (x+3)\right ) \log \left (\frac {4096 \log (x+3)}{x^2 \left (-9 x^4+18 x^3-9 x^2+64\right )^2}\right )}{1408 \left (3 x^2-3 x+8\right ) \log (x+3)}\right )dx\) |
Int[((128*x - 18*x^3 + 36*x^4 - 18*x^5 + (-768 - 256*x + 324*x^2 - 756*x^3 + 252*x^4 + 180*x^5)*Log[3 + x])*Log[(4096*Log[3 + x])/(4096*x^2 - 1152*x ^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10)])/((-192 *x - 64*x^2 + 27*x^3 - 45*x^4 + 9*x^5 + 9*x^6)*Log[3 + x]),x]
3.10.46.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Int[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[ {v = RationalFunctionExpand[u/(a + b*x^n + c*x^(2*n)), x]}, Int[v, x] /; Su mQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]
Leaf count of result is larger than twice the leaf count of optimal. \(104\) vs. \(2(37)=74\).
Time = 37.57 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.50
| method | result | size |
| default | \(-\ln \left (\frac {\ln \left (3+x \right )}{x^{2} \left (81 \left (3+x \right )^{8}-2268 \left (3+x \right )^{7}+27702 \left (3+x \right )^{6}-192780 \left (3+x \right )^{5}+834849 \left (3+x \right )^{4}-2297232 \left (3+x \right )^{3}+3904992 \left (3+x \right )^{2}-9658880-3725568 x \right )}\right )^{2}+24 \ln \left (2\right ) \left (-\ln \left (\ln \left (3+x \right )\right )+2 \ln \left (\left (9 x^{4}-18 x^{3}+9 x^{2}-64\right ) x \right )\right )\) | \(105\) |
int(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*ln(3+x)-18*x^5+36*x^4-18* x^3+128*x)*ln(4096*ln(3+x)/(81*x^10-324*x^9+486*x^8-324*x^7-1071*x^6+2304* x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ln(3+x),x ,method=_RETURNVERBOSE)
-ln(ln(3+x)/x^2/(81*(3+x)^8-2268*(3+x)^7+27702*(3+x)^6-192780*(3+x)^5+8348 49*(3+x)^4-2297232*(3+x)^3+3904992*(3+x)^2-9658880-3725568*x))^2+24*ln(2)* (-ln(ln(3+x))+2*ln((9*x^4-18*x^3+9*x^2-64)*x))
Time = 0.25 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.80 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=-\log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right )^{2} \]
integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36* x^4-18*x^3+128*x)*log(4096*log(3+x)/(81*x^10-324*x^9+486*x^8-324*x^7-1071* x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ log(3+x),x, algorithm=\
-log(4096*log(x + 3)/(81*x^10 - 324*x^9 + 486*x^8 - 324*x^7 - 1071*x^6 + 2 304*x^5 - 1152*x^4 + 4096*x^2))^2
Time = 0.32 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=- \log {\left (\frac {4096 \log {\left (x + 3 \right )}}{81 x^{10} - 324 x^{9} + 486 x^{8} - 324 x^{7} - 1071 x^{6} + 2304 x^{5} - 1152 x^{4} + 4096 x^{2}} \right )}^{2} \]
integrate(((180*x**5+252*x**4-756*x**3+324*x**2-256*x-768)*ln(3+x)-18*x**5 +36*x**4-18*x**3+128*x)*ln(4096*ln(3+x)/(81*x**10-324*x**9+486*x**8-324*x* *7-1071*x**6+2304*x**5-1152*x**4+4096*x**2))/(9*x**6+9*x**5-45*x**4+27*x** 3-64*x**2-192*x)/ln(3+x),x)
-log(4096*log(x + 3)/(81*x**10 - 324*x**9 + 486*x**8 - 324*x**7 - 1071*x** 6 + 2304*x**5 - 1152*x**4 + 4096*x**2))**2
Leaf count of result is larger than twice the leaf count of optimal. 206 vs. \(2 (31) = 62\).
Time = 0.23 (sec) , antiderivative size = 206, normalized size of antiderivative = 6.87 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=4 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x + 8\right )^{2} + 4 \, {\left (2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x - 8\right )^{2} + 4 \, \log \left (x\right )^{2} + 2 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right ) - 4 \, \log \left (x\right ) \log \left (\log \left (x + 3\right )\right ) + \log \left (\log \left (x + 3\right )\right )^{2} \]
integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36* x^4-18*x^3+128*x)*log(4096*log(3+x)/(81*x^10-324*x^9+486*x^8-324*x^7-1071* x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ log(3+x),x, algorithm=\
4*(2*log(3*x^2 - 3*x - 8) + 2*log(x) - log(log(x + 3)))*log(3*x^2 - 3*x + 8) + 4*log(3*x^2 - 3*x + 8)^2 + 4*(2*log(x) - log(log(x + 3)))*log(3*x^2 - 3*x - 8) + 4*log(3*x^2 - 3*x - 8)^2 + 4*log(x)^2 + 2*(2*log(3*x^2 - 3*x + 8) + 2*log(3*x^2 - 3*x - 8) + 2*log(x) - log(log(x + 3)))*log(4096*log(x + 3)/(81*x^10 - 324*x^9 + 486*x^8 - 324*x^7 - 1071*x^6 + 2304*x^5 - 1152*x ^4 + 4096*x^2)) - 4*log(x)*log(log(x + 3)) + log(log(x + 3))^2
Leaf count of result is larger than twice the leaf count of optimal. 207 vs. \(2 (31) = 62\).
Time = 0.44 (sec) , antiderivative size = 207, normalized size of antiderivative = 6.90 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=-2 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}\right ) + 4 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) - 4 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right )^{2} + 4 \, \log \left (x\right )^{2} + 4 \, {\left (\log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + \log \left (x\right )\right )} \log \left (4096 \, \log \left (x + 3\right )\right ) - \log \left (4096 \, \log \left (x + 3\right )\right )^{2} - 4 \, \log \left (x\right ) \log \left (\log \left (x + 3\right )\right ) \]
integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36* x^4-18*x^3+128*x)*log(4096*log(3+x)/(81*x^10-324*x^9+486*x^8-324*x^7-1071* x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ log(3+x),x, algorithm=\
-2*(2*log(9*x^4 - 18*x^3 + 9*x^2 - 64) + 2*log(x) - log(log(x + 3)))*log(8 1*x^10 - 324*x^9 + 486*x^8 - 324*x^7 - 1071*x^6 + 2304*x^5 - 1152*x^4 + 40 96*x^2) + 4*(2*log(9*x^4 - 18*x^3 + 9*x^2 - 64) + 2*log(x) - log(log(x + 3 )))*log(9*x^4 - 18*x^3 + 9*x^2 - 64) - 4*log(9*x^4 - 18*x^3 + 9*x^2 - 64)^ 2 + 4*log(x)^2 + 4*(log(9*x^4 - 18*x^3 + 9*x^2 - 64) + log(x))*log(4096*lo g(x + 3)) - log(4096*log(x + 3))^2 - 4*log(x)*log(log(x + 3))
Time = 10.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.80 \[ \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx=-{\ln \left (\frac {4096\,\ln \left (x+3\right )}{81\,x^{10}-324\,x^9+486\,x^8-324\,x^7-1071\,x^6+2304\,x^5-1152\,x^4+4096\,x^2}\right )}^2 \]
int((log((4096*log(x + 3))/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 32 4*x^7 + 486*x^8 - 324*x^9 + 81*x^10))*(log(x + 3)*(256*x - 324*x^2 + 756*x ^3 - 252*x^4 - 180*x^5 + 768) - 128*x + 18*x^3 - 36*x^4 + 18*x^5))/(log(x + 3)*(192*x + 64*x^2 - 27*x^3 + 45*x^4 - 9*x^5 - 9*x^6)),x)