Integrand size = 231, antiderivative size = 27 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=\frac {10 \log (4+x)}{5-\left (x-\frac {8-\log (2)}{x}\right )^2} \] Output:
10*ln(4+x)/(5-(x-(8-ln(2))/x)^2)
Time = 5.05 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=-\frac {10 x^2 \log (4+x)}{x^4+(-8+\log (2))^2+x^2 (-21+\log (4))} \] Input:
Integrate[(-640*x^2 + 210*x^4 - 10*x^6 + (160*x^2 - 20*x^4)*Log[2] - 10*x^ 2*Log[2]^2 + (-5120*x - 1280*x^2 + 80*x^5 + 20*x^6 + (1280*x + 320*x^2)*Lo g[2] + (-80*x - 20*x^2)*Log[2]^2)*Log[4 + x])/(16384 + 4096*x - 10752*x^2 - 2688*x^3 + 2276*x^4 + 569*x^5 - 168*x^6 - 42*x^7 + 4*x^8 + x^9 + (-8192 - 2048*x + 3712*x^2 + 928*x^3 - 464*x^4 - 116*x^5 + 16*x^6 + 4*x^7)*Log[2] + (1536 + 384*x - 424*x^2 - 106*x^3 + 24*x^4 + 6*x^5)*Log[2]^2 + (-128 - 32*x + 16*x^2 + 4*x^3)*Log[2]^3 + (4 + x)*Log[2]^4),x]
Output:
(-10*x^2*Log[4 + x])/(x^4 + (-8 + Log[2])^2 + x^2*(-21 + Log[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.
| \(\displaystyle \int \frac {-10 x^6+210 x^4-640 x^2-10 x^2 \log ^2(2)+\left (160 x^2-20 x^4\right ) \log (2)+\left (20 x^6+80 x^5-1280 x^2+\left (-20 x^2-80 x\right ) \log ^2(2)+\left (320 x^2+1280 x\right ) \log (2)-5120 x\right ) \log (x+4)}{x^9+4 x^8-42 x^7-168 x^6+569 x^5+2276 x^4-2688 x^3-10752 x^2+\left (4 x^3+16 x^2-32 x-128\right ) \log ^3(2)+\left (6 x^5+24 x^4-106 x^3-424 x^2+384 x+1536\right ) \log ^2(2)+\left (4 x^7+16 x^6-116 x^5-464 x^4+928 x^3+3712 x^2-2048 x-8192\right ) \log (2)+4096 x+(x+4) \log ^4(2)+16384} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-10 x^6+210 x^4+x^2 \left (-640-10 \log ^2(2)\right )+\left (160 x^2-20 x^4\right ) \log (2)+\left (20 x^6+80 x^5-1280 x^2+\left (-20 x^2-80 x\right ) \log ^2(2)+\left (320 x^2+1280 x\right ) \log (2)-5120 x\right ) \log (x+4)}{x^9+4 x^8-42 x^7-168 x^6+569 x^5+2276 x^4-2688 x^3-10752 x^2+\left (4 x^3+16 x^2-32 x-128\right ) \log ^3(2)+\left (6 x^5+24 x^4-106 x^3-424 x^2+384 x+1536\right ) \log ^2(2)+\left (4 x^7+16 x^6-116 x^5-464 x^4+928 x^3+3712 x^2-2048 x-8192\right ) \log (2)+4096 x+(x+4) \log ^4(2)+16384}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {(4-x) \left (-x^2+5-\log (4)\right ) \left (-10 x^6+210 x^4+x^2 \left (-640-10 \log ^2(2)\right )+\left (160 x^2-20 x^4\right ) \log (2)+\left (20 x^6+80 x^5-1280 x^2+\left (-20 x^2-80 x\right ) \log ^2(2)+\left (320 x^2+1280 x\right ) \log (2)-5120 x\right ) \log (x+4)\right )}{\left (16-\log ^2(2)-16 \log (2)\right ) \left (x^4-x^2 (21-\log (4))+(\log (2)-8)^2\right )^2}+\frac {(4-x) \left (x^2-5+\log (4)\right ) \left (-10 x^6+210 x^4+x^2 \left (-640-10 \log ^2(2)\right )+\left (160 x^2-20 x^4\right ) \log (2)+\left (20 x^6+80 x^5-1280 x^2+\left (-20 x^2-80 x\right ) \log ^2(2)+\left (320 x^2+1280 x\right ) \log (2)-5120 x\right ) \log (x+4)\right )}{\left (16-\log ^2(2)-16 \log (2)\right )^2 \left (x^4-x^2 (21-\log (4))+(\log (2)-8)^2\right )}+\frac {-10 x^6+210 x^4+x^2 \left (-640-10 \log ^2(2)\right )+\left (160 x^2-20 x^4\right ) \log (2)+\left (20 x^6+80 x^5-1280 x^2+\left (-20 x^2-80 x\right ) \log ^2(2)+\left (320 x^2+1280 x\right ) \log (2)-5120 x\right ) \log (x+4)}{(x+4) \left (-16+\log ^2(2)+16 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {10 x \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \left (x^5-2 (x+4) \left (x^4-(\log (2)-8)^2\right ) \log (x+4)+x^3 (\log (4)-21)+x (\log (2)-8)^2\right )}{(x+4) \left (16-\log ^2(2)-16 \log (2)\right )^2 \left (x^4+x^2 (\log (4)-21)+(\log (2)-8)^2\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5-(21-\log (4)) x^3+(8-\log (2))^2 x-2 (x+4) \left (x^4-(8-\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \left (\frac {x^6}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(-21+\log (4)) x^4}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {(8-\log (2))^2 x^2}{(x+4) \left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}+\frac {2 \left (-x^2-\log (2)+8\right ) \left (x^2-\log (2)+8\right ) \log (x+4) x}{\left (x^4-(21-\log (4)) x^2+(-8+\log (2))^2\right )^2}\right )dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {10 \left (-\log ^4(2)+32 \log ^3(2)-32 \log ^2(2) (7+\log (4))+2048 \log (2)-256 (1+\log (64))\right ) \int \frac {x \left (x^5+(-21+\log (4)) x^3+(-8+\log (2))^2 x-2 (x+4) \left (x^4-(-8+\log (2))^2\right ) \log (x+4)\right )}{(x+4) \left (x^4+(-21+\log (4)) x^2+(-8+\log (2))^2\right )^2}dx}{\left (16-\log ^2(2)-16 \log (2)\right )^2}\) |
Input:
Int[(-640*x^2 + 210*x^4 - 10*x^6 + (160*x^2 - 20*x^4)*Log[2] - 10*x^2*Log[ 2]^2 + (-5120*x - 1280*x^2 + 80*x^5 + 20*x^6 + (1280*x + 320*x^2)*Log[2] + (-80*x - 20*x^2)*Log[2]^2)*Log[4 + x])/(16384 + 4096*x - 10752*x^2 - 2688 *x^3 + 2276*x^4 + 569*x^5 - 168*x^6 - 42*x^7 + 4*x^8 + x^9 + (-8192 - 2048 *x + 3712*x^2 + 928*x^3 - 464*x^4 - 116*x^5 + 16*x^6 + 4*x^7)*Log[2] + (15 36 + 384*x - 424*x^2 - 106*x^3 + 24*x^4 + 6*x^5)*Log[2]^2 + (-128 - 32*x + 16*x^2 + 4*x^3)*Log[2]^3 + (4 + x)*Log[2]^4),x]
Output:
$Aborted
Time = 2.75 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37
| method | result | size |
| norman | \(-\frac {10 x^{2} \ln \left (4+x \right )}{x^{4}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}-21 x^{2}-16 \ln \left (2\right )+64}\) | \(37\) |
| risch | \(-\frac {10 x^{2} \ln \left (4+x \right )}{x^{4}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}-21 x^{2}-16 \ln \left (2\right )+64}\) | \(37\) |
| parallelrisch | \(-\frac {10 x^{2} \ln \left (4+x \right )}{x^{4}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}-21 x^{2}-16 \ln \left (2\right )+64}\) | \(37\) |
| derivativedivides | \(-\frac {10 \ln \left (4+x \right ) \left (4+x \right ) \left (\ln \left (2\right )^{2} \left (4+x \right )-16 \left (4+x \right )^{3}-8 \ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+256 \left (4+x \right )^{2}+128 \ln \left (2\right )-3328-1216 x \right )}{\left (\ln \left (2\right )^{2}+16 \ln \left (2\right )-16\right ) \left (\left (4+x \right )^{4}+2 \ln \left (2\right ) \left (4+x \right )^{2}-16 \left (4+x \right )^{3}+\ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+75 \left (4+x \right )^{2}+16 \ln \left (2\right )-368-88 x \right )}-\frac {160 \ln \left (4+x \right )}{\ln \left (2\right )^{2}+16 \ln \left (2\right )-16}\) | \(135\) |
| default | \(-\frac {10 \ln \left (4+x \right ) \left (4+x \right ) \left (\ln \left (2\right )^{2} \left (4+x \right )-16 \left (4+x \right )^{3}-8 \ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+256 \left (4+x \right )^{2}+128 \ln \left (2\right )-3328-1216 x \right )}{\left (\ln \left (2\right )^{2}+16 \ln \left (2\right )-16\right ) \left (\left (4+x \right )^{4}+2 \ln \left (2\right ) \left (4+x \right )^{2}-16 \left (4+x \right )^{3}+\ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+75 \left (4+x \right )^{2}+16 \ln \left (2\right )-368-88 x \right )}-\frac {160 \ln \left (4+x \right )}{\ln \left (2\right )^{2}+16 \ln \left (2\right )-16}\) | \(135\) |
| parts | \(-\frac {160 \ln \left (4+x \right )}{\ln \left (2\right )^{2}+16 \ln \left (2\right )-16}-\frac {10 \left (\frac {\frac {\left (-\ln \left (2\right )^{2}-8 \sqrt {-20 \ln \left (2\right )+185}+104\right ) \ln \left (2 x^{2}+2 \ln \left (2\right )+\sqrt {-20 \ln \left (2\right )+185}-21\right )}{2}-\frac {2 \left (4 \ln \left (2\right )^{2}+32 \sqrt {-20 \ln \left (2\right )+185}-416\right ) \operatorname {arctanh}\left (\frac {2 x}{\sqrt {42-4 \ln \left (2\right )-2 \sqrt {-20 \ln \left (2\right )+185}}}\right )}{\sqrt {42-4 \ln \left (2\right )-2 \sqrt {-20 \ln \left (2\right )+185}}}}{\sqrt {-20 \ln \left (2\right )+185}}+\frac {\frac {\left (\ln \left (2\right )^{2}-8 \sqrt {-20 \ln \left (2\right )+185}-104\right ) \ln \left (2 x^{2}+2 \ln \left (2\right )-\sqrt {-20 \ln \left (2\right )+185}-21\right )}{2}-\frac {2 \left (-4 \ln \left (2\right )^{2}+32 \sqrt {-20 \ln \left (2\right )+185}+416\right ) \operatorname {arctanh}\left (\frac {2 x}{\sqrt {42-4 \ln \left (2\right )+2 \sqrt {-20 \ln \left (2\right )+185}}}\right )}{\sqrt {42-4 \ln \left (2\right )+2 \sqrt {-20 \ln \left (2\right )+185}}}}{\sqrt {-20 \ln \left (2\right )+185}}\right )}{\ln \left (2\right )^{2}+16 \ln \left (2\right )-16}+\frac {5 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}-16 \textit {\_Z}^{3}+\left (2 \ln \left (2\right )+75\right ) \textit {\_Z}^{2}+\left (-16 \ln \left (2\right )-88\right ) \textit {\_Z} +\ln \left (2\right )^{2}+16 \ln \left (2\right )-16\right )}{\sum }\frac {\left (-16 \textit {\_R}^{3}+256 \textit {\_R}^{2}+\left (\ln \left (2\right )^{2}-16 \ln \left (2\right )-1216\right ) \textit {\_R} -8 \ln \left (2\right )^{2}+128 \ln \left (2\right )+1536\right ) \ln \left (4+x -\textit {\_R} \right )}{-44+2 \textit {\_R}^{3}+2 \ln \left (2\right ) \textit {\_R} -24 \textit {\_R}^{2}-8 \ln \left (2\right )+75 \textit {\_R}}\right )}{\ln \left (2\right )^{2}+16 \ln \left (2\right )-16}-\frac {10 \ln \left (4+x \right ) \left (4+x \right ) \left (\ln \left (2\right )^{2} \left (4+x \right )-16 \left (4+x \right )^{3}-8 \ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+256 \left (4+x \right )^{2}+128 \ln \left (2\right )-3328-1216 x \right )}{\left (\ln \left (2\right )^{2}+16 \ln \left (2\right )-16\right ) \left (\left (4+x \right )^{4}+2 \ln \left (2\right ) \left (4+x \right )^{2}-16 \left (4+x \right )^{3}+\ln \left (2\right )^{2}-16 \ln \left (2\right ) \left (4+x \right )+75 \left (4+x \right )^{2}+16 \ln \left (2\right )-368-88 x \right )}\) | \(494\) |
Input:
int((((-20*x^2-80*x)*ln(2)^2+(320*x^2+1280*x)*ln(2)+20*x^6+80*x^5-1280*x^2 -5120*x)*ln(4+x)-10*x^2*ln(2)^2+(-20*x^4+160*x^2)*ln(2)-10*x^6+210*x^4-640 *x^2)/((4+x)*ln(2)^4+(4*x^3+16*x^2-32*x-128)*ln(2)^3+(6*x^5+24*x^4-106*x^3 -424*x^2+384*x+1536)*ln(2)^2+(4*x^7+16*x^6-116*x^5-464*x^4+928*x^3+3712*x^ 2-2048*x-8192)*ln(2)+x^9+4*x^8-42*x^7-168*x^6+569*x^5+2276*x^4-2688*x^3-10 752*x^2+4096*x+16384),x,method=_RETURNVERBOSE)
Output:
-10*x^2*ln(4+x)/(x^4+2*x^2*ln(2)+ln(2)^2-21*x^2-16*ln(2)+64)
Time = 0.09 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=-\frac {10 \, x^{2} \log \left (x + 4\right )}{x^{4} - 21 \, x^{2} + 2 \, {\left (x^{2} - 8\right )} \log \left (2\right ) + \log \left (2\right )^{2} + 64} \] Input:
integrate((((-20*x^2-80*x)*log(2)^2+(320*x^2+1280*x)*log(2)+20*x^6+80*x^5- 1280*x^2-5120*x)*log(4+x)-10*x^2*log(2)^2+(-20*x^4+160*x^2)*log(2)-10*x^6+ 210*x^4-640*x^2)/((4+x)*log(2)^4+(4*x^3+16*x^2-32*x-128)*log(2)^3+(6*x^5+2 4*x^4-106*x^3-424*x^2+384*x+1536)*log(2)^2+(4*x^7+16*x^6-116*x^5-464*x^4+9 28*x^3+3712*x^2-2048*x-8192)*log(2)+x^9+4*x^8-42*x^7-168*x^6+569*x^5+2276* x^4-2688*x^3-10752*x^2+4096*x+16384),x, algorithm="fricas")
Output:
-10*x^2*log(x + 4)/(x^4 - 21*x^2 + 2*(x^2 - 8)*log(2) + log(2)^2 + 64)
Leaf count of result is larger than twice the leaf count of optimal. 39 vs. \(2 (17) = 34\).
Time = 0.60 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=- \frac {10 x^{2} \log {\left (x + 4 \right )}}{x^{4} - 21 x^{2} + 2 x^{2} \log {\left (2 \right )} - 16 \log {\left (2 \right )} + \log {\left (2 \right )}^{2} + 64} \] Input:
integrate((((-20*x**2-80*x)*ln(2)**2+(320*x**2+1280*x)*ln(2)+20*x**6+80*x* *5-1280*x**2-5120*x)*ln(4+x)-10*x**2*ln(2)**2+(-20*x**4+160*x**2)*ln(2)-10 *x**6+210*x**4-640*x**2)/((4+x)*ln(2)**4+(4*x**3+16*x**2-32*x-128)*ln(2)** 3+(6*x**5+24*x**4-106*x**3-424*x**2+384*x+1536)*ln(2)**2+(4*x**7+16*x**6-1 16*x**5-464*x**4+928*x**3+3712*x**2-2048*x-8192)*ln(2)+x**9+4*x**8-42*x**7 -168*x**6+569*x**5+2276*x**4-2688*x**3-10752*x**2+4096*x+16384),x)
Output:
-10*x**2*log(x + 4)/(x**4 - 21*x**2 + 2*x**2*log(2) - 16*log(2) + log(2)** 2 + 64)
Time = 0.13 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=-\frac {10 \, x^{2} \log \left (x + 4\right )}{x^{4} + x^{2} {\left (2 \, \log \left (2\right ) - 21\right )} + \log \left (2\right )^{2} - 16 \, \log \left (2\right ) + 64} \] Input:
integrate((((-20*x^2-80*x)*log(2)^2+(320*x^2+1280*x)*log(2)+20*x^6+80*x^5- 1280*x^2-5120*x)*log(4+x)-10*x^2*log(2)^2+(-20*x^4+160*x^2)*log(2)-10*x^6+ 210*x^4-640*x^2)/((4+x)*log(2)^4+(4*x^3+16*x^2-32*x-128)*log(2)^3+(6*x^5+2 4*x^4-106*x^3-424*x^2+384*x+1536)*log(2)^2+(4*x^7+16*x^6-116*x^5-464*x^4+9 28*x^3+3712*x^2-2048*x-8192)*log(2)+x^9+4*x^8-42*x^7-168*x^6+569*x^5+2276* x^4-2688*x^3-10752*x^2+4096*x+16384),x, algorithm="maxima")
Output:
-10*x^2*log(x + 4)/(x^4 + x^2*(2*log(2) - 21) + log(2)^2 - 16*log(2) + 64)
Time = 0.24 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=-\frac {10 \, x^{2} \log \left (x + 4\right )}{x^{4} + 2 \, x^{2} \log \left (2\right ) - 21 \, x^{2} + \log \left (2\right )^{2} - 16 \, \log \left (2\right ) + 64} \] Input:
integrate((((-20*x^2-80*x)*log(2)^2+(320*x^2+1280*x)*log(2)+20*x^6+80*x^5- 1280*x^2-5120*x)*log(4+x)-10*x^2*log(2)^2+(-20*x^4+160*x^2)*log(2)-10*x^6+ 210*x^4-640*x^2)/((4+x)*log(2)^4+(4*x^3+16*x^2-32*x-128)*log(2)^3+(6*x^5+2 4*x^4-106*x^3-424*x^2+384*x+1536)*log(2)^2+(4*x^7+16*x^6-116*x^5-464*x^4+9 28*x^3+3712*x^2-2048*x-8192)*log(2)+x^9+4*x^8-42*x^7-168*x^6+569*x^5+2276* x^4-2688*x^3-10752*x^2+4096*x+16384),x, algorithm="giac")
Output:
-10*x^2*log(x + 4)/(x^4 + 2*x^2*log(2) - 21*x^2 + log(2)^2 - 16*log(2) + 6 4)
Timed out. \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=\text {Hanged} \] Input:
int(-(10*x^2*log(2)^2 + log(x + 4)*(5120*x - log(2)*(1280*x + 320*x^2) + l og(2)^2*(80*x + 20*x^2) + 1280*x^2 - 80*x^5 - 20*x^6) - log(2)*(160*x^2 - 20*x^4) + 640*x^2 - 210*x^4 + 10*x^6)/(4096*x + log(2)^4*(x + 4) + log(2)^ 2*(384*x - 424*x^2 - 106*x^3 + 24*x^4 + 6*x^5 + 1536) - log(2)*(2048*x - 3 712*x^2 - 928*x^3 + 464*x^4 + 116*x^5 - 16*x^6 - 4*x^7 + 8192) - log(2)^3* (32*x - 16*x^2 - 4*x^3 + 128) - 10752*x^2 - 2688*x^3 + 2276*x^4 + 569*x^5 - 168*x^6 - 42*x^7 + 4*x^8 + x^9 + 16384),x)
Output:
\text{Hanged}
Time = 0.30 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-640 x^2+210 x^4-10 x^6+\left (160 x^2-20 x^4\right ) \log (2)-10 x^2 \log ^2(2)+\left (-5120 x-1280 x^2+80 x^5+20 x^6+\left (1280 x+320 x^2\right ) \log (2)+\left (-80 x-20 x^2\right ) \log ^2(2)\right ) \log (4+x)}{16384+4096 x-10752 x^2-2688 x^3+2276 x^4+569 x^5-168 x^6-42 x^7+4 x^8+x^9+\left (-8192-2048 x+3712 x^2+928 x^3-464 x^4-116 x^5+16 x^6+4 x^7\right ) \log (2)+\left (1536+384 x-424 x^2-106 x^3+24 x^4+6 x^5\right ) \log ^2(2)+\left (-128-32 x+16 x^2+4 x^3\right ) \log ^3(2)+(4+x) \log ^4(2)} \, dx=-\frac {10 \,\mathrm {log}\left (x +4\right ) x^{2}}{\mathrm {log}\left (2\right )^{2}+2 \,\mathrm {log}\left (2\right ) x^{2}-16 \,\mathrm {log}\left (2\right )+x^{4}-21 x^{2}+64} \] Input:
int((((-20*x^2-80*x)*log(2)^2+(320*x^2+1280*x)*log(2)+20*x^6+80*x^5-1280*x ^2-5120*x)*log(4+x)-10*x^2*log(2)^2+(-20*x^4+160*x^2)*log(2)-10*x^6+210*x^ 4-640*x^2)/((4+x)*log(2)^4+(4*x^3+16*x^2-32*x-128)*log(2)^3+(6*x^5+24*x^4- 106*x^3-424*x^2+384*x+1536)*log(2)^2+(4*x^7+16*x^6-116*x^5-464*x^4+928*x^3 +3712*x^2-2048*x-8192)*log(2)+x^9+4*x^8-42*x^7-168*x^6+569*x^5+2276*x^4-26 88*x^3-10752*x^2+4096*x+16384),x)
Output:
( - 10*log(x + 4)*x**2)/(log(2)**2 + 2*log(2)*x**2 - 16*log(2) + x**4 - 21 *x**2 + 64)