Integrand size = 344, antiderivative size = 33 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=\left (9-e^x+x\right )^2 \left (-x-\log (x)+\frac {\log (x)}{1-x^2}\right )^2 \] Output:
(ln(x)/(-x^2+1)-ln(x)-x)^2*(x+9-exp(x))^2
Time = 0.11 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=\frac {x^2 \left (9-e^x+x\right )^2 \left (-1+x^2+x \log (x)\right )^2}{\left (-1+x^2\right )^2} \] Input:
Integrate[(-162*x + 108*x^2 + 518*x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^ 7 + 56*x^8 + 4*x^9 + E^(2*x)*(-2*x + 6*x^3 + 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x^8) + E^x*(36*x - 12*x^2 - 110*x^3 + 110*x^5 + 36*x^6 - 34*x^7 - 24* x^8 - 2*x^9) + (486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6 *x^8 + E^(2*x)*(6*x^2 + 2*x^3 - 8*x^4 - 6*x^5 + 2*x^6 + 4*x^7) + E^x*(-108 *x^2 - 16*x^3 + 144*x^4 + 60*x^5 - 32*x^6 - 44*x^7 - 4*x^8))*Log[x] + (-32 4*x^3 - 90*x^4 - 6*x^5 + 18*x^6 + 2*x^7 + E^(2*x)*(-4*x^3 - 2*x^4 + 2*x^6) + E^x*(72*x^3 + 28*x^4 + 2*x^5 - 20*x^6 - 2*x^7))*Log[x]^2)/(-1 + 3*x^2 - 3*x^4 + x^6),x]
Output:
(x^2*(9 - E^x + x)^2*(-1 + x^2 + x*Log[x])^2)/(-1 + x^2)^2
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {4 x^9+56 x^8+186 x^7-4 x^6-546 x^5-160 x^4+518 x^3+108 x^2+\left (2 x^7+18 x^6-6 x^5-90 x^4-324 x^3+e^{2 x} \left (2 x^6-2 x^4-4 x^3\right )+e^x \left (-2 x^7-20 x^6+2 x^5+28 x^4+72 x^3\right )\right ) \log ^2(x)+e^{2 x} \left (2 x^8+2 x^7-4 x^6-6 x^5+2 x^4+6 x^3-2 x\right )+e^x \left (-2 x^9-24 x^8-34 x^7+36 x^6+110 x^5-110 x^3-12 x^2+36 x\right )+\left (6 x^8+74 x^7+182 x^6-56 x^5-674 x^4-18 x^3+486 x^2+e^{2 x} \left (4 x^7+2 x^6-6 x^5-8 x^4+2 x^3+6 x^2\right )+e^x \left (-4 x^8-44 x^7-32 x^6+60 x^5+144 x^4-16 x^3-108 x^2\right )\right ) \log (x)-162 x}{x^6-3 x^4+3 x^2-1} \, dx\) |
| \(\Big \downarrow \) 2070 |
| \(\displaystyle \int \frac {4 x^9+56 x^8+186 x^7-4 x^6-546 x^5-160 x^4+518 x^3+108 x^2+\left (2 x^7+18 x^6-6 x^5-90 x^4-324 x^3+e^{2 x} \left (2 x^6-2 x^4-4 x^3\right )+e^x \left (-2 x^7-20 x^6+2 x^5+28 x^4+72 x^3\right )\right ) \log ^2(x)+e^{2 x} \left (2 x^8+2 x^7-4 x^6-6 x^5+2 x^4+6 x^3-2 x\right )+e^x \left (-2 x^9-24 x^8-34 x^7+36 x^6+110 x^5-110 x^3-12 x^2+36 x\right )+\left (6 x^8+74 x^7+182 x^6-56 x^5-674 x^4-18 x^3+486 x^2+e^{2 x} \left (4 x^7+2 x^6-6 x^5-8 x^4+2 x^3+6 x^2\right )+e^x \left (-4 x^8-44 x^7-32 x^6+60 x^5+144 x^4-16 x^3-108 x^2\right )\right ) \log (x)-162 x}{\left (x^2-1\right )^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (x-e^x+9\right ) \left (-x^2-x \log (x)+1\right ) \left (-x \left (-x^3+e^x \left (x^3-x-2\right )+3 x+18\right ) \log (x)-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2+e^x \left (x^3+x^2-1\right )-7 x+9\right )\right )\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (\left (1-x^2\right ) \left (-2 x^3-10 x^2-7 x-e^x \left (-x^3-x^2+1\right )+9\right )-x \left (-x^3+3 x-e^x \left (-x^3+x+2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {x \left (x-e^x+9\right ) \left (-x^2-\log (x) x+1\right ) \left (-\left (\left (x^2-1\right ) \left (-2 x^3-10 x^2-7 x+e^x \left (x^3+x^2-1\right )+9\right )\right )-x \left (-x^3+3 x+e^x \left (x^3-x-2\right )+18\right ) \log (x)\right )}{\left (1-x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {\log (x) \left (x^2+\log (x) x-1\right ) x^6}{\left (x^2-1\right )^3}+\frac {9 \log (x) \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^3}+\frac {2 \left (x^2+\log (x) x-1\right ) x^5}{\left (x^2-1\right )^2}-\frac {3 \log (x) \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^3}+\frac {28 \left (x^2+\log (x) x-1\right ) x^4}{\left (x^2-1\right )^2}-\frac {45 \log (x) \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^3}+\frac {97 \left (x^2+\log (x) x-1\right ) x^3}{\left (x^2-1\right )^2}-\frac {162 \log (x) \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^3}+\frac {54 \left (x^2+\log (x) x-1\right ) x^2}{\left (x^2-1\right )^2}-\frac {81 \left (x^2+\log (x) x-1\right ) x}{\left (x^2-1\right )^2}+\frac {e^{2 x} \left (x^2+\log (x) x-1\right ) \left (x^5+\log (x) x^4+x^4-x^3-\log (x) x^2-2 x^2-2 \log (x) x+1\right ) x}{\left (x^2-1\right )^3}-\frac {e^x \left (x^8+2 \log (x) x^7+12 x^7+\log ^2(x) x^6+22 \log (x) x^6+17 x^6+10 \log ^2(x) x^5+16 \log (x) x^5-18 x^5-\log ^2(x) x^4-30 \log (x) x^4-55 x^4-14 \log ^2(x) x^3-72 \log (x) x^3-36 \log ^2(x) x^2+8 \log (x) x^2+55 x^2+54 \log (x) x+6 x-18\right ) x}{\left (x^2-1\right )^3}\right )dx\) |
Input:
Int[(-162*x + 108*x^2 + 518*x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^7 + 56 *x^8 + 4*x^9 + E^(2*x)*(-2*x + 6*x^3 + 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x ^8) + E^x*(36*x - 12*x^2 - 110*x^3 + 110*x^5 + 36*x^6 - 34*x^7 - 24*x^8 - 2*x^9) + (486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6*x^8 + E^(2*x)*(6*x^2 + 2*x^3 - 8*x^4 - 6*x^5 + 2*x^6 + 4*x^7) + E^x*(-108*x^2 - 16*x^3 + 144*x^4 + 60*x^5 - 32*x^6 - 44*x^7 - 4*x^8))*Log[x] + (-324*x^3 - 90*x^4 - 6*x^5 + 18*x^6 + 2*x^7 + E^(2*x)*(-4*x^3 - 2*x^4 + 2*x^6) + E^x *(72*x^3 + 28*x^4 + 2*x^5 - 20*x^6 - 2*x^7))*Log[x]^2)/(-1 + 3*x^2 - 3*x^4 + x^6),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(129\) vs. \(2(32)=64\).
Time = 0.17 (sec) , antiderivative size = 130, normalized size of antiderivative = 3.94
\[\frac {\left (x^{2}-2 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}+18 x -18 \,{\mathrm e}^{x}+81\right ) x^{4} \ln \left (x \right )^{2}}{\left (x^{2}-1\right )^{2}}+\frac {2 \left (x^{5}-2 \,{\mathrm e}^{x} x^{4}+{\mathrm e}^{2 x} x^{3}+18 x^{4}-18 \,{\mathrm e}^{x} x^{3}+81 x^{3}-18 x^{2}+18\right ) \ln \left (x \right )}{x^{2}-1}+x^{4}-2 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x} x^{2}+18 x^{3}-18 \,{\mathrm e}^{x} x^{2}+81 x^{2}+36 \ln \left (x \right )\]
Input:
int((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp (x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^3)*ln(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+2 *x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-108*x^2)* exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*ln(x)+(2*x^8+2* x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+110 *x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^5-160*x^ 4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x)
Output:
(x^2-2*exp(x)*x+exp(x)^2+18*x-18*exp(x)+81)*x^4/(x^2-1)^2*ln(x)^2+2*(x^5-2 *exp(x)*x^4+exp(x)^2*x^3+18*x^4-18*exp(x)*x^3+81*x^3-18*x^2+18)/(x^2-1)*ln (x)+x^4-2*exp(x)*x^3+exp(x)^2*x^2+18*x^3-18*exp(x)*x^2+81*x^2+36*ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 200 vs. \(2 (26) = 52\).
Time = 0.08 (sec) , antiderivative size = 200, normalized size of antiderivative = 6.06 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=\frac {x^{8} + 18 \, x^{7} + 79 \, x^{6} - 36 \, x^{5} - 161 \, x^{4} + 18 \, x^{3} + {\left (x^{6} + 18 \, x^{5} + x^{4} e^{\left (2 \, x\right )} + 81 \, x^{4} - 2 \, {\left (x^{5} + 9 \, x^{4}\right )} e^{x}\right )} \log \left (x\right )^{2} + 81 \, x^{2} + {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + 9 \, x^{2}\right )} e^{x} + 2 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 18 \, x^{4} - 81 \, x^{3} + {\left (x^{5} - x^{3}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} e^{x}\right )} \log \left (x\right )}{x^{4} - 2 \, x^{2} + 1} \] Input:
integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^ 3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5- 8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-10 8*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+( 2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36 *x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^ 5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="fricas" )
Output:
(x^8 + 18*x^7 + 79*x^6 - 36*x^5 - 161*x^4 + 18*x^3 + (x^6 + 18*x^5 + x^4*e ^(2*x) + 81*x^4 - 2*(x^5 + 9*x^4)*e^x)*log(x)^2 + 81*x^2 + (x^6 - 2*x^4 + x^2)*e^(2*x) - 2*(x^7 + 9*x^6 - 2*x^5 - 18*x^4 + x^3 + 9*x^2)*e^x + 2*(x^7 + 18*x^6 + 80*x^5 - 18*x^4 - 81*x^3 + (x^5 - x^3)*e^(2*x) - 2*(x^6 + 9*x^ 5 - x^4 - 9*x^3)*e^x)*log(x))/(x^4 - 2*x^2 + 1)
Leaf count of result is larger than twice the leaf count of optimal. 369 vs. \(2 (22) = 44\).
Time = 0.46 (sec) , antiderivative size = 369, normalized size of antiderivative = 11.18 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=x^{4} + 18 x^{3} + 81 x^{2} + \frac {\left (x^{10} + 2 x^{9} \log {\left (x \right )} + x^{8} \log {\left (x \right )}^{2} - 4 x^{8} - 6 x^{7} \log {\left (x \right )} - 2 x^{6} \log {\left (x \right )}^{2} + 6 x^{6} + 6 x^{5} \log {\left (x \right )} + x^{4} \log {\left (x \right )}^{2} - 4 x^{4} - 2 x^{3} \log {\left (x \right )} + x^{2}\right ) e^{2 x} + \left (- 2 x^{11} - 4 x^{10} \log {\left (x \right )} - 18 x^{10} - 2 x^{9} \log {\left (x \right )}^{2} - 36 x^{9} \log {\left (x \right )} + 8 x^{9} - 18 x^{8} \log {\left (x \right )}^{2} + 12 x^{8} \log {\left (x \right )} + 72 x^{8} + 4 x^{7} \log {\left (x \right )}^{2} + 108 x^{7} \log {\left (x \right )} - 12 x^{7} + 36 x^{6} \log {\left (x \right )}^{2} - 12 x^{6} \log {\left (x \right )} - 108 x^{6} - 2 x^{5} \log {\left (x \right )}^{2} - 108 x^{5} \log {\left (x \right )} + 8 x^{5} - 18 x^{4} \log {\left (x \right )}^{2} + 4 x^{4} \log {\left (x \right )} + 72 x^{4} + 36 x^{3} \log {\left (x \right )} - 2 x^{3} - 18 x^{2}\right ) e^{x}}{x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1} + 36 \log {\left (x \right )} + \frac {\left (x^{6} + 18 x^{5} + 81 x^{4}\right ) \log {\left (x \right )}^{2}}{x^{4} - 2 x^{2} + 1} + \frac {\left (2 x^{5} + 36 x^{4} + 162 x^{3} - 36 x^{2} + 36\right ) \log {\left (x \right )}}{x^{2} - 1} \] Input:
integrate((((2*x**6-2*x**4-4*x**3)*exp(x)**2+(-2*x**7-20*x**6+2*x**5+28*x* *4+72*x**3)*exp(x)+2*x**7+18*x**6-6*x**5-90*x**4-324*x**3)*ln(x)**2+((4*x* *7+2*x**6-6*x**5-8*x**4+2*x**3+6*x**2)*exp(x)**2+(-4*x**8-44*x**7-32*x**6+ 60*x**5+144*x**4-16*x**3-108*x**2)*exp(x)+6*x**8+74*x**7+182*x**6-56*x**5- 674*x**4-18*x**3+486*x**2)*ln(x)+(2*x**8+2*x**7-4*x**6-6*x**5+2*x**4+6*x** 3-2*x)*exp(x)**2+(-2*x**9-24*x**8-34*x**7+36*x**6+110*x**5-110*x**3-12*x** 2+36*x)*exp(x)+4*x**9+56*x**8+186*x**7-4*x**6-546*x**5-160*x**4+518*x**3+1 08*x**2-162*x)/(x**6-3*x**4+3*x**2-1),x)
Output:
x**4 + 18*x**3 + 81*x**2 + ((x**10 + 2*x**9*log(x) + x**8*log(x)**2 - 4*x* *8 - 6*x**7*log(x) - 2*x**6*log(x)**2 + 6*x**6 + 6*x**5*log(x) + x**4*log( x)**2 - 4*x**4 - 2*x**3*log(x) + x**2)*exp(2*x) + (-2*x**11 - 4*x**10*log( x) - 18*x**10 - 2*x**9*log(x)**2 - 36*x**9*log(x) + 8*x**9 - 18*x**8*log(x )**2 + 12*x**8*log(x) + 72*x**8 + 4*x**7*log(x)**2 + 108*x**7*log(x) - 12* x**7 + 36*x**6*log(x)**2 - 12*x**6*log(x) - 108*x**6 - 2*x**5*log(x)**2 - 108*x**5*log(x) + 8*x**5 - 18*x**4*log(x)**2 + 4*x**4*log(x) + 72*x**4 + 3 6*x**3*log(x) - 2*x**3 - 18*x**2)*exp(x))/(x**8 - 4*x**6 + 6*x**4 - 4*x**2 + 1) + 36*log(x) + (x**6 + 18*x**5 + 81*x**4)*log(x)**2/(x**4 - 2*x**2 + 1) + (2*x**5 + 36*x**4 + 162*x**3 - 36*x**2 + 36)*log(x)/(x**2 - 1)
Leaf count of result is larger than twice the leaf count of optimal. 436 vs. \(2 (26) = 52\).
Time = 0.12 (sec) , antiderivative size = 436, normalized size of antiderivative = 13.21 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=x^{4} + \frac {56}{3} \, x^{3} + 99 \, x^{2} + 164 \, x - \frac {2 \, x^{7} + 54 \, x^{6} + 488 \, x^{5} - 108 \, x^{4} - 982 \, x^{3} - 3 \, {\left (x^{6} + 18 \, x^{5} + 81 \, x^{4}\right )} \log \left (x\right )^{2} + 54 \, x^{2} - 3 \, {\left (x^{6} + x^{4} \log \left (x\right )^{2} - 2 \, x^{4} + x^{2} + 2 \, {\left (x^{5} - x^{3}\right )} \log \left (x\right )\right )} e^{\left (2 \, x\right )} + 6 \, {\left (x^{7} + 9 \, x^{6} - 2 \, x^{5} - 18 \, x^{4} + x^{3} + {\left (x^{5} + 9 \, x^{4}\right )} \log \left (x\right )^{2} + 9 \, x^{2} + 2 \, {\left (x^{6} + 9 \, x^{5} - x^{4} - 9 \, x^{3}\right )} \log \left (x\right )\right )} e^{x} - 6 \, {\left (x^{7} + 18 \, x^{6} + 80 \, x^{5} - 36 \, x^{4} - 81 \, x^{3} + 36 \, x^{2} - 18\right )} \log \left (x\right ) + 492 \, x}{3 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {7 \, {\left (13 \, x^{3} - 11 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} + \frac {9 \, x^{3} - 7 \, x}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {20 \, {\left (5 \, x^{3} - 3 \, x\right )}}{x^{4} - 2 \, x^{2} + 1} - \frac {27 \, {\left (x^{3} + x\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {8 \, x^{2} - 7}{x^{4} - 2 \, x^{2} + 1} - \frac {93 \, {\left (6 \, x^{2} - 5\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {273 \, {\left (4 \, x^{2} - 3\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} - \frac {259 \, {\left (2 \, x^{2} - 1\right )}}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + \frac {81}{2 \, {\left (x^{4} - 2 \, x^{2} + 1\right )}} + 18 \, \log \left (x^{2} - 1\right ) - 18 \, \log \left (x + 1\right ) - 18 \, \log \left (x - 1\right ) + 36 \, \log \left (x\right ) \] Input:
integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^ 3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5- 8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-10 8*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+( 2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36 *x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^ 5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="maxima" )
Output:
x^4 + 56/3*x^3 + 99*x^2 + 164*x - 1/3*(2*x^7 + 54*x^6 + 488*x^5 - 108*x^4 - 982*x^3 - 3*(x^6 + 18*x^5 + 81*x^4)*log(x)^2 + 54*x^2 - 3*(x^6 + x^4*log (x)^2 - 2*x^4 + x^2 + 2*(x^5 - x^3)*log(x))*e^(2*x) + 6*(x^7 + 9*x^6 - 2*x ^5 - 18*x^4 + x^3 + (x^5 + 9*x^4)*log(x)^2 + 9*x^2 + 2*(x^6 + 9*x^5 - x^4 - 9*x^3)*log(x))*e^x - 6*(x^7 + 18*x^6 + 80*x^5 - 36*x^4 - 81*x^3 + 36*x^2 - 18)*log(x) + 492*x)/(x^4 - 2*x^2 + 1) - 7*(13*x^3 - 11*x)/(x^4 - 2*x^2 + 1) + 1/2*(9*x^3 - 7*x)/(x^4 - 2*x^2 + 1) + 20*(5*x^3 - 3*x)/(x^4 - 2*x^2 + 1) - 27/2*(x^3 + x)/(x^4 - 2*x^2 + 1) - (8*x^2 - 7)/(x^4 - 2*x^2 + 1) - 93/2*(6*x^2 - 5)/(x^4 - 2*x^2 + 1) + 273/2*(4*x^2 - 3)/(x^4 - 2*x^2 + 1) - 259/2*(2*x^2 - 1)/(x^4 - 2*x^2 + 1) + 81/2/(x^4 - 2*x^2 + 1) + 18*log(x^ 2 - 1) - 18*log(x + 1) - 18*log(x - 1) + 36*log(x)
\[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=\int { \frac {2 \, {\left (2 \, x^{9} + 28 \, x^{8} + 93 \, x^{7} - 2 \, x^{6} - 273 \, x^{5} - 80 \, x^{4} + 259 \, x^{3} + {\left (x^{7} + 9 \, x^{6} - 3 \, x^{5} - 45 \, x^{4} - 162 \, x^{3} + {\left (x^{6} - x^{4} - 2 \, x^{3}\right )} e^{\left (2 \, x\right )} - {\left (x^{7} + 10 \, x^{6} - x^{5} - 14 \, x^{4} - 36 \, x^{3}\right )} e^{x}\right )} \log \left (x\right )^{2} + 54 \, x^{2} + {\left (x^{8} + x^{7} - 2 \, x^{6} - 3 \, x^{5} + x^{4} + 3 \, x^{3} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{9} + 12 \, x^{8} + 17 \, x^{7} - 18 \, x^{6} - 55 \, x^{5} + 55 \, x^{3} + 6 \, x^{2} - 18 \, x\right )} e^{x} + {\left (3 \, x^{8} + 37 \, x^{7} + 91 \, x^{6} - 28 \, x^{5} - 337 \, x^{4} - 9 \, x^{3} + 243 \, x^{2} + {\left (2 \, x^{7} + x^{6} - 3 \, x^{5} - 4 \, x^{4} + x^{3} + 3 \, x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{8} + 11 \, x^{7} + 8 \, x^{6} - 15 \, x^{5} - 36 \, x^{4} + 4 \, x^{3} + 27 \, x^{2}\right )} e^{x}\right )} \log \left (x\right ) - 81 \, x\right )}}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1} \,d x } \] Input:
integrate((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^ 3)*exp(x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5- 8*x^4+2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-10 8*x^2)*exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+( 2*x^8+2*x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36 *x^6+110*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^ 5-160*x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x, algorithm="giac")
Output:
integrate(2*(2*x^9 + 28*x^8 + 93*x^7 - 2*x^6 - 273*x^5 - 80*x^4 + 259*x^3 + (x^7 + 9*x^6 - 3*x^5 - 45*x^4 - 162*x^3 + (x^6 - x^4 - 2*x^3)*e^(2*x) - (x^7 + 10*x^6 - x^5 - 14*x^4 - 36*x^3)*e^x)*log(x)^2 + 54*x^2 + (x^8 + x^7 - 2*x^6 - 3*x^5 + x^4 + 3*x^3 - x)*e^(2*x) - (x^9 + 12*x^8 + 17*x^7 - 18* x^6 - 55*x^5 + 55*x^3 + 6*x^2 - 18*x)*e^x + (3*x^8 + 37*x^7 + 91*x^6 - 28* x^5 - 337*x^4 - 9*x^3 + 243*x^2 + (2*x^7 + x^6 - 3*x^5 - 4*x^4 + x^3 + 3*x ^2)*e^(2*x) - 2*(x^8 + 11*x^7 + 8*x^6 - 15*x^5 - 36*x^4 + 4*x^3 + 27*x^2)* e^x)*log(x) - 81*x)/(x^6 - 3*x^4 + 3*x^2 - 1), x)
Time = 2.77 (sec) , antiderivative size = 316, normalized size of antiderivative = 9.58 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=81\,{\ln \left (x\right )}^2-2\,x^3\,{\mathrm {e}}^x-18\,x^2\,{\mathrm {e}}^x-\frac {81\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}+x^2\,{\mathrm {e}}^{2\,x}+81\,x^2+18\,x^3+x^4+{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2+\frac {162\,x^2\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}+\frac {18\,x^5\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}+\frac {x^6\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}-\frac {{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}+\frac {162\,x^3\,\ln \left (x\right )}{x^2-1}+\frac {36\,x^4\,\ln \left (x\right )}{x^2-1}+\frac {2\,x^5\,\ln \left (x\right )}{x^2-1}-\frac {18\,x^4\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}-\frac {2\,x^5\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}+\frac {2\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \left (x\right )}^2}{x^4-2\,x^2+1}-\frac {36\,x^3\,{\mathrm {e}}^x\,\ln \left (x\right )}{x^2-1}-\frac {4\,x^4\,{\mathrm {e}}^x\,\ln \left (x\right )}{x^2-1}+\frac {2\,x^3\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right )}{x^2-1} \] Input:
int((exp(2*x)*(6*x^3 - 2*x + 2*x^4 - 6*x^5 - 4*x^6 + 2*x^7 + 2*x^8) - 162* x - log(x)^2*(exp(2*x)*(4*x^3 + 2*x^4 - 2*x^6) - exp(x)*(72*x^3 + 28*x^4 + 2*x^5 - 20*x^6 - 2*x^7) + 324*x^3 + 90*x^4 + 6*x^5 - 18*x^6 - 2*x^7) + lo g(x)*(exp(2*x)*(6*x^2 + 2*x^3 - 8*x^4 - 6*x^5 + 2*x^6 + 4*x^7) - exp(x)*(1 08*x^2 + 16*x^3 - 144*x^4 - 60*x^5 + 32*x^6 + 44*x^7 + 4*x^8) + 486*x^2 - 18*x^3 - 674*x^4 - 56*x^5 + 182*x^6 + 74*x^7 + 6*x^8) + 108*x^2 + 518*x^3 - 160*x^4 - 546*x^5 - 4*x^6 + 186*x^7 + 56*x^8 + 4*x^9 - exp(x)*(12*x^2 - 36*x + 110*x^3 - 110*x^5 - 36*x^6 + 34*x^7 + 24*x^8 + 2*x^9))/(3*x^2 - 3*x ^4 + x^6 - 1),x)
Output:
81*log(x)^2 - 2*x^3*exp(x) - 18*x^2*exp(x) - (81*log(x)^2)/(x^4 - 2*x^2 + 1) + x^2*exp(2*x) + 81*x^2 + 18*x^3 + x^4 + exp(2*x)*log(x)^2 + (162*x^2*l og(x)^2)/(x^4 - 2*x^2 + 1) + (18*x^5*log(x)^2)/(x^4 - 2*x^2 + 1) + (x^6*lo g(x)^2)/(x^4 - 2*x^2 + 1) - (exp(2*x)*log(x)^2)/(x^4 - 2*x^2 + 1) + (162*x ^3*log(x))/(x^2 - 1) + (36*x^4*log(x))/(x^2 - 1) + (2*x^5*log(x))/(x^2 - 1 ) - (18*x^4*exp(x)*log(x)^2)/(x^4 - 2*x^2 + 1) - (2*x^5*exp(x)*log(x)^2)/( x^4 - 2*x^2 + 1) + (2*x^2*exp(2*x)*log(x)^2)/(x^4 - 2*x^2 + 1) - (36*x^3*e xp(x)*log(x))/(x^2 - 1) - (4*x^4*exp(x)*log(x))/(x^2 - 1) + (2*x^3*exp(2*x )*log(x))/(x^2 - 1)
Time = 0.21 (sec) , antiderivative size = 286, normalized size of antiderivative = 8.67 \[ \int \frac {-162 x+108 x^2+518 x^3-160 x^4-546 x^5-4 x^6+186 x^7+56 x^8+4 x^9+e^{2 x} \left (-2 x+6 x^3+2 x^4-6 x^5-4 x^6+2 x^7+2 x^8\right )+e^x \left (36 x-12 x^2-110 x^3+110 x^5+36 x^6-34 x^7-24 x^8-2 x^9\right )+\left (486 x^2-18 x^3-674 x^4-56 x^5+182 x^6+74 x^7+6 x^8+e^{2 x} \left (6 x^2+2 x^3-8 x^4-6 x^5+2 x^6+4 x^7\right )+e^x \left (-108 x^2-16 x^3+144 x^4+60 x^5-32 x^6-44 x^7-4 x^8\right )\right ) \log (x)+\left (-324 x^3-90 x^4-6 x^5+18 x^6+2 x^7+e^{2 x} \left (-4 x^3-2 x^4+2 x^6\right )+e^x \left (72 x^3+28 x^4+2 x^5-20 x^6-2 x^7\right )\right ) \log ^2(x)}{-1+3 x^2-3 x^4+x^6} \, dx=\frac {-9+81 \mathrm {log}\left (x \right )^{2} x^{4}+18 \mathrm {log}\left (x \right )^{2} x^{5}-2 e^{x} x^{7}+e^{2 x} \mathrm {log}\left (x \right )^{2} x^{4}+e^{2 x} x^{2}+36 e^{x} x^{4}-2 e^{x} x^{3}+36 e^{x} \mathrm {log}\left (x \right ) x^{3}+4 e^{x} x^{5}-36 \,\mathrm {log}\left (x \right ) x^{4}+99 x^{2}-2 e^{2 x} \mathrm {log}\left (x \right ) x^{3}+e^{2 x} x^{6}-36 x^{5}+18 x^{7}+18 x^{3}+\mathrm {log}\left (x \right )^{2} x^{6}+2 \,\mathrm {log}\left (x \right ) x^{7}+36 \,\mathrm {log}\left (x \right ) x^{6}-18 e^{x} x^{6}-2 e^{2 x} x^{4}-18 e^{x} x^{2}+x^{8}+79 x^{6}+160 \,\mathrm {log}\left (x \right ) x^{5}-162 \,\mathrm {log}\left (x \right ) x^{3}-170 x^{4}+2 e^{2 x} \mathrm {log}\left (x \right ) x^{5}-2 e^{x} \mathrm {log}\left (x \right )^{2} x^{5}-18 e^{x} \mathrm {log}\left (x \right )^{2} x^{4}-4 e^{x} \mathrm {log}\left (x \right ) x^{6}-36 e^{x} \mathrm {log}\left (x \right ) x^{5}+4 e^{x} \mathrm {log}\left (x \right ) x^{4}}{x^{4}-2 x^{2}+1} \] Input:
int((((2*x^6-2*x^4-4*x^3)*exp(x)^2+(-2*x^7-20*x^6+2*x^5+28*x^4+72*x^3)*exp (x)+2*x^7+18*x^6-6*x^5-90*x^4-324*x^3)*log(x)^2+((4*x^7+2*x^6-6*x^5-8*x^4+ 2*x^3+6*x^2)*exp(x)^2+(-4*x^8-44*x^7-32*x^6+60*x^5+144*x^4-16*x^3-108*x^2) *exp(x)+6*x^8+74*x^7+182*x^6-56*x^5-674*x^4-18*x^3+486*x^2)*log(x)+(2*x^8+ 2*x^7-4*x^6-6*x^5+2*x^4+6*x^3-2*x)*exp(x)^2+(-2*x^9-24*x^8-34*x^7+36*x^6+1 10*x^5-110*x^3-12*x^2+36*x)*exp(x)+4*x^9+56*x^8+186*x^7-4*x^6-546*x^5-160* x^4+518*x^3+108*x^2-162*x)/(x^6-3*x^4+3*x^2-1),x)
Output:
(e**(2*x)*log(x)**2*x**4 + 2*e**(2*x)*log(x)*x**5 - 2*e**(2*x)*log(x)*x**3 + e**(2*x)*x**6 - 2*e**(2*x)*x**4 + e**(2*x)*x**2 - 2*e**x*log(x)**2*x**5 - 18*e**x*log(x)**2*x**4 - 4*e**x*log(x)*x**6 - 36*e**x*log(x)*x**5 + 4*e **x*log(x)*x**4 + 36*e**x*log(x)*x**3 - 2*e**x*x**7 - 18*e**x*x**6 + 4*e** x*x**5 + 36*e**x*x**4 - 2*e**x*x**3 - 18*e**x*x**2 + log(x)**2*x**6 + 18*l og(x)**2*x**5 + 81*log(x)**2*x**4 + 2*log(x)*x**7 + 36*log(x)*x**6 + 160*l og(x)*x**5 - 36*log(x)*x**4 - 162*log(x)*x**3 + x**8 + 18*x**7 + 79*x**6 - 36*x**5 - 170*x**4 + 18*x**3 + 99*x**2 - 9)/(x**4 - 2*x**2 + 1)