Integrand size = 196, antiderivative size = 32 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=2+\frac {1}{x}+x-\frac {\log (x) \left (1-\log \left (4-x+\frac {x}{-4+x^2}\right )\right )}{x^2} \]
Time = 0.11 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=\frac {1}{x}+x-\frac {\log (x)}{x^2}+\frac {\log (x) \log \left (-\frac {16-5 x-4 x^2+x^3}{-4+x^2}\right )}{x^2} \]
Integrate[(64 + 44*x - 52*x^2 - 87*x^3 + 33*x^4 + 35*x^5 - 10*x^6 - 4*x^7 + x^8 + (-64 + 20*x + 32*x^2 - 9*x^3 - 4*x^4 + x^5)*Log[(-16 + 5*x + 4*x^2 - x^3)/(-4 + x^2)] + Log[x]*(-128 + 60*x + 64*x^2 - 25*x^3 - 8*x^4 + 3*x^ 5 + (128 - 40*x - 64*x^2 + 18*x^3 + 8*x^4 - 2*x^5)*Log[(-16 + 5*x + 4*x^2 - x^3)/(-4 + x^2)]))/(-64*x^3 + 20*x^4 + 32*x^5 - 9*x^6 - 4*x^7 + x^8),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.
| \(\displaystyle \int \frac {x^8-4 x^7-10 x^6+35 x^5+33 x^4-87 x^3-52 x^2+\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2+\left (-2 x^5+8 x^4+18 x^3-64 x^2-40 x+128\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+60 x-128\right )+44 x+64}{x^8-4 x^7-9 x^6+32 x^5+20 x^4-64 x^3} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {x^8-4 x^7-10 x^6+35 x^5+33 x^4-87 x^3-52 x^2+\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2+\left (-2 x^5+8 x^4+18 x^3-64 x^2-40 x+128\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+60 x-128\right )+44 x+64}{x^3 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (x^2-4 x-1\right ) \left (x^8-4 x^7-10 x^6+35 x^5+33 x^4-87 x^3-52 x^2+\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2+\left (-2 x^5+8 x^4+18 x^3-64 x^2-40 x+128\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+60 x-128\right )+44 x+64\right )}{4 x^3 \left (x^3-4 x^2-5 x+16\right )}-\frac {x^8-4 x^7-10 x^6+35 x^5+33 x^4-87 x^3-52 x^2+\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2+\left (-2 x^5+8 x^4+18 x^3-64 x^2-40 x+128\right ) \log \left (\frac {-x^3+4 x^2+5 x-16}{x^2-4}\right )+60 x-128\right )+44 x+64}{4 x^2 \left (x^2-4\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{x^3 \left (4-x^2\right ) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\left (\left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \left (x^3+\log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )-x-1\right )\right )-\log (x) \left (3 x^5-8 x^4-25 x^3+64 x^2-2 \left (x^5-4 x^4-9 x^3+32 x^2+20 x-64\right ) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )+60 x-128\right )}{(2-x) x^3 (x+2) \left (x^3-4 x^2-5 x+16\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {1}{x^2}+\frac {4 x}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {9}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {32}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}-\frac {20}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}+\frac {64}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}+\frac {3 x^2 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {8 x \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}-\frac {25 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right )}+\frac {64 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x}+\frac {60 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^2}-\frac {128 \log (x)}{(x-2) (x+2) \left (x^3-4 x^2-5 x+16\right ) x^3}-\frac {(2 \log (x)-1) \log \left (-\frac {x^3-4 x^2-5 x+16}{x^2-4}\right )}{x^3}-\frac {x^2}{x^5-4 x^4-9 x^3+32 x^2+20 x-64}+1\right )dx\) |
Int[(64 + 44*x - 52*x^2 - 87*x^3 + 33*x^4 + 35*x^5 - 10*x^6 - 4*x^7 + x^8 + (-64 + 20*x + 32*x^2 - 9*x^3 - 4*x^4 + x^5)*Log[(-16 + 5*x + 4*x^2 - x^3 )/(-4 + x^2)] + Log[x]*(-128 + 60*x + 64*x^2 - 25*x^3 - 8*x^4 + 3*x^5 + (1 28 - 40*x - 64*x^2 + 18*x^3 + 8*x^4 - 2*x^5)*Log[(-16 + 5*x + 4*x^2 - x^3) /(-4 + x^2)]))/(-64*x^3 + 20*x^4 + 32*x^5 - 9*x^6 - 4*x^7 + x^8),x]
3.1.91.3.1 Defintions of rubi rules used
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_)), x_Symbol] :> With[{v = RationalFunctionE xpand[u/(a + b*x^n), x]}, Int[v, x] /; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ [n, 0]
Time = 12.88 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.59
| method | result | size |
| parallelrisch | \(-\frac {-19992 x^{3}-20139 x^{2}-19992 \ln \left (-\frac {x^{3}-4 x^{2}-5 x +16}{x^{2}-4}\right ) \ln \left (x \right )-19992 x +19992 \ln \left (x \right )}{19992 x^{2}}\) | \(51\) |
| risch | \(\frac {\ln \left (x \right ) \ln \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}}+\frac {-2 i \pi {\operatorname {csgn}\left (\frac {i \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}-4}\right )}^{2} \ln \left (x \right )-i \pi \,\operatorname {csgn}\left (\frac {i}{x^{2}-4}\right ) \operatorname {csgn}\left (i \left (x^{3}-4 x^{2}-5 x +16\right )\right ) \operatorname {csgn}\left (\frac {i \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}-4}\right ) \ln \left (x \right )+i \pi \,\operatorname {csgn}\left (\frac {i}{x^{2}-4}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}-4}\right )}^{2} \ln \left (x \right )+i \pi \,\operatorname {csgn}\left (i \left (x^{3}-4 x^{2}-5 x +16\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}-4}\right )}^{2} \ln \left (x \right )+i \pi {\operatorname {csgn}\left (\frac {i \left (x^{3}-4 x^{2}-5 x +16\right )}{x^{2}-4}\right )}^{3} \ln \left (x \right )+2 i \ln \left (x \right ) \pi +2 x^{3}-2 \ln \left (x \right ) \ln \left (x^{2}-4\right )+2 x -2 \ln \left (x \right )}{2 x^{2}}\) | \(270\) |
int((((-2*x^5+8*x^4+18*x^3-64*x^2-40*x+128)*ln((-x^3+4*x^2+5*x-16)/(x^2-4) )+3*x^5-8*x^4-25*x^3+64*x^2+60*x-128)*ln(x)+(x^5-4*x^4-9*x^3+32*x^2+20*x-6 4)*ln((-x^3+4*x^2+5*x-16)/(x^2-4))+x^8-4*x^7-10*x^6+35*x^5+33*x^4-87*x^3-5 2*x^2+44*x+64)/(x^8-4*x^7-9*x^6+32*x^5+20*x^4-64*x^3),x,method=_RETURNVERB OSE)
-1/19992/x^2*(-19992*x^3-20139*x^2-19992*ln(-(x^3-4*x^2-5*x+16)/(x^2-4))*l n(x)-19992*x+19992*ln(x))
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=\frac {x^{3} + {\left (\log \left (-\frac {x^{3} - 4 \, x^{2} - 5 \, x + 16}{x^{2} - 4}\right ) - 1\right )} \log \left (x\right ) + x}{x^{2}} \]
integrate((((-2*x^5+8*x^4+18*x^3-64*x^2-40*x+128)*log((-x^3+4*x^2+5*x-16)/ (x^2-4))+3*x^5-8*x^4-25*x^3+64*x^2+60*x-128)*log(x)+(x^5-4*x^4-9*x^3+32*x^ 2+20*x-64)*log((-x^3+4*x^2+5*x-16)/(x^2-4))+x^8-4*x^7-10*x^6+35*x^5+33*x^4 -87*x^3-52*x^2+44*x+64)/(x^8-4*x^7-9*x^6+32*x^5+20*x^4-64*x^3),x, algorith m=\
Time = 0.42 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=x + \frac {1}{x} + \frac {\log {\left (x \right )} \log {\left (\frac {- x^{3} + 4 x^{2} + 5 x - 16}{x^{2} - 4} \right )}}{x^{2}} - \frac {\log {\left (x \right )}}{x^{2}} \]
integrate((((-2*x**5+8*x**4+18*x**3-64*x**2-40*x+128)*ln((-x**3+4*x**2+5*x -16)/(x**2-4))+3*x**5-8*x**4-25*x**3+64*x**2+60*x-128)*ln(x)+(x**5-4*x**4- 9*x**3+32*x**2+20*x-64)*ln((-x**3+4*x**2+5*x-16)/(x**2-4))+x**8-4*x**7-10* x**6+35*x**5+33*x**4-87*x**3-52*x**2+44*x+64)/(x**8-4*x**7-9*x**6+32*x**5+ 20*x**4-64*x**3),x)
Time = 0.21 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.50 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=\frac {x^{3} + \log \left (-x^{3} + 4 \, x^{2} + 5 \, x - 16\right ) \log \left (x\right ) - \log \left (x + 2\right ) \log \left (x\right ) - \log \left (x - 2\right ) \log \left (x\right ) + x - \log \left (x\right )}{x^{2}} \]
integrate((((-2*x^5+8*x^4+18*x^3-64*x^2-40*x+128)*log((-x^3+4*x^2+5*x-16)/ (x^2-4))+3*x^5-8*x^4-25*x^3+64*x^2+60*x-128)*log(x)+(x^5-4*x^4-9*x^3+32*x^ 2+20*x-64)*log((-x^3+4*x^2+5*x-16)/(x^2-4))+x^8-4*x^7-10*x^6+35*x^5+33*x^4 -87*x^3-52*x^2+44*x+64)/(x^8-4*x^7-9*x^6+32*x^5+20*x^4-64*x^3),x, algorith m=\
(x^3 + log(-x^3 + 4*x^2 + 5*x - 16)*log(x) - log(x + 2)*log(x) - log(x - 2 )*log(x) + x - log(x))/x^2
Time = 0.39 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.47 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=x + \frac {\log \left (-x^{3} + 4 \, x^{2} + 5 \, x - 16\right ) \log \left (x\right )}{x^{2}} - \frac {\log \left (x^{2} - 4\right ) \log \left (x\right )}{x^{2}} + \frac {1}{x} - \frac {\log \left (x\right )}{x^{2}} \]
integrate((((-2*x^5+8*x^4+18*x^3-64*x^2-40*x+128)*log((-x^3+4*x^2+5*x-16)/ (x^2-4))+3*x^5-8*x^4-25*x^3+64*x^2+60*x-128)*log(x)+(x^5-4*x^4-9*x^3+32*x^ 2+20*x-64)*log((-x^3+4*x^2+5*x-16)/(x^2-4))+x^8-4*x^7-10*x^6+35*x^5+33*x^4 -87*x^3-52*x^2+44*x+64)/(x^8-4*x^7-9*x^6+32*x^5+20*x^4-64*x^3),x, algorith m=\
Time = 13.43 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.31 \[ \int \frac {64+44 x-52 x^2-87 x^3+33 x^4+35 x^5-10 x^6-4 x^7+x^8+\left (-64+20 x+32 x^2-9 x^3-4 x^4+x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )+\log (x) \left (-128+60 x+64 x^2-25 x^3-8 x^4+3 x^5+\left (128-40 x-64 x^2+18 x^3+8 x^4-2 x^5\right ) \log \left (\frac {-16+5 x+4 x^2-x^3}{-4+x^2}\right )\right )}{-64 x^3+20 x^4+32 x^5-9 x^6-4 x^7+x^8} \, dx=x-\frac {\ln \left (x\right )}{x^2}+\frac {1}{x}+\frac {\ln \left (\frac {-x^3+4\,x^2+5\,x-16}{x^2-4}\right )\,\ln \left (x\right )}{x^2} \]
int(-(44*x + log((5*x + 4*x^2 - x^3 - 16)/(x^2 - 4))*(20*x + 32*x^2 - 9*x^ 3 - 4*x^4 + x^5 - 64) - log(x)*(log((5*x + 4*x^2 - x^3 - 16)/(x^2 - 4))*(4 0*x + 64*x^2 - 18*x^3 - 8*x^4 + 2*x^5 - 128) - 60*x - 64*x^2 + 25*x^3 + 8* x^4 - 3*x^5 + 128) - 52*x^2 - 87*x^3 + 33*x^4 + 35*x^5 - 10*x^6 - 4*x^7 + x^8 + 64)/(64*x^3 - 20*x^4 - 32*x^5 + 9*x^6 + 4*x^7 - x^8),x)