Integrand size = 293, antiderivative size = 33 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {x^2}{\frac {5}{3-x}+x-\frac {5+e^x+\frac {2}{x^2}}{\log (x)}} \] Output:
x^2/(5/(3-x)+x-(2/x^2+5+exp(x))/ln(x))
Time = 0.09 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.27 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {(-3+x) x^4 \log (x)}{-\left ((-3+x) \left (2+\left (5+e^x\right ) x^2\right )\right )+x^2 \left (-5-3 x+x^2\right ) \log (x)} \] Input:
Integrate[(-18*x^3 + 12*x^4 - 47*x^5 + 30*x^6 - 5*x^7 + E^x*(-9*x^5 + 6*x^ 6 - x^7) + (-72*x^3 + 48*x^4 - 98*x^5 + 60*x^6 - 10*x^7 + E^x*(-18*x^5 + 2 1*x^6 - 8*x^7 + x^8))*Log[x] + (30*x^5 - 6*x^6 - 6*x^7 + x^8)*Log[x]^2)/(3 6 - 24*x + 184*x^2 - 120*x^3 + 245*x^4 - 150*x^5 + 25*x^6 + E^(2*x)*(9*x^4 - 6*x^5 + x^6) + E^x*(36*x^2 - 24*x^3 + 94*x^4 - 60*x^5 + 10*x^6) + (-60* x^2 - 16*x^3 - 126*x^4 - 44*x^5 + 60*x^6 - 10*x^7 + E^x*(-30*x^4 - 8*x^5 + 12*x^6 - 2*x^7))*Log[x] + (25*x^4 + 30*x^5 - x^6 - 6*x^7 + x^8)*Log[x]^2) ,x]
Output:
((-3 + x)*x^4*Log[x])/(-((-3 + x)*(2 + (5 + E^x)*x^2)) + x^2*(-5 - 3*x + x ^2)*Log[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.
| \(\displaystyle \int \frac {-5 x^7+30 x^6-47 x^5+12 x^4-18 x^3+e^x \left (-x^7+6 x^6-9 x^5\right )+\left (x^8-6 x^7-6 x^6+30 x^5\right ) \log ^2(x)+\left (-10 x^7+60 x^6-98 x^5+48 x^4-72 x^3+e^x \left (x^8-8 x^7+21 x^6-18 x^5\right )\right ) \log (x)}{25 x^6-150 x^5+245 x^4-120 x^3+184 x^2+e^{2 x} \left (x^6-6 x^5+9 x^4\right )+\left (x^8-6 x^7-x^6+30 x^5+25 x^4\right ) \log ^2(x)+e^x \left (10 x^6-60 x^5+94 x^4-24 x^3+36 x^2\right )+\left (-10 x^7+60 x^6-44 x^5-126 x^4-16 x^3-60 x^2+e^x \left (-2 x^7+12 x^6-8 x^5-30 x^4\right )\right ) \log (x)-24 x+36} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 \left (-\left (\left (\left (e^x+5\right ) x^2+2\right ) (x-3)^2\right )+x^2 \left (x^3-6 x^2-6 x+30\right ) \log ^2(x)+\left (e^x x^3-2 \left (e^x+5\right ) x^2-8\right ) (x-3)^2 \log (x)\right )}{\left ((x-3) \left (\left (e^x+5\right ) x^2+2\right )+\left (-x^2+3 x+5\right ) x^2 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^3 \log (x) \left (x^6 \log (x)-6 x^5-7 x^5 \log (x)+36 x^4+10 x^4 \log (x)-51 x^3+x^3 \log (x)-7 x^2+6 x-36\right )}{\left (x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6\right )^2}-\frac {(x-3) x^3 (x \log (x)-2 \log (x)-1)}{x^4 \log (x)-e^x x^3-5 x^3-3 x^3 \log (x)+3 e^x x^2+15 x^2-5 x^2 \log (x)-2 x+6}\right )dx\) |
Input:
Int[(-18*x^3 + 12*x^4 - 47*x^5 + 30*x^6 - 5*x^7 + E^x*(-9*x^5 + 6*x^6 - x^ 7) + (-72*x^3 + 48*x^4 - 98*x^5 + 60*x^6 - 10*x^7 + E^x*(-18*x^5 + 21*x^6 - 8*x^7 + x^8))*Log[x] + (30*x^5 - 6*x^6 - 6*x^7 + x^8)*Log[x]^2)/(36 - 24 *x + 184*x^2 - 120*x^3 + 245*x^4 - 150*x^5 + 25*x^6 + E^(2*x)*(9*x^4 - 6*x ^5 + x^6) + E^x*(36*x^2 - 24*x^3 + 94*x^4 - 60*x^5 + 10*x^6) + (-60*x^2 - 16*x^3 - 126*x^4 - 44*x^5 + 60*x^6 - 10*x^7 + E^x*(-30*x^4 - 8*x^5 + 12*x^ 6 - 2*x^7))*Log[x] + (25*x^4 + 30*x^5 - x^6 - 6*x^7 + x^8)*Log[x]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(123\) vs. \(2(32)=64\).
Time = 0.04 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.76
\[\frac {x^{2} \left (-3+x \right )}{x^{2}-3 x -5}+\frac {x^{2} \left ({\mathrm e}^{x} x^{4}+5 x^{4}-6 \,{\mathrm e}^{x} x^{3}-30 x^{3}+9 \,{\mathrm e}^{x} x^{2}+47 x^{2}-12 x +18\right )}{\left (x^{2}-3 x -5\right ) \left (x^{4} \ln \left (x \right )-{\mathrm e}^{x} x^{3}-3 x^{3} \ln \left (x \right )-5 x^{3}+3 \,{\mathrm e}^{x} x^{2}-5 x^{2} \ln \left (x \right )+15 x^{2}-2 x +6\right )}\]
Input:
int(((x^8-6*x^7-6*x^6+30*x^5)*ln(x)^2+((x^8-8*x^7+21*x^6-18*x^5)*exp(x)-10 *x^7+60*x^6-98*x^5+48*x^4-72*x^3)*ln(x)+(-x^7+6*x^6-9*x^5)*exp(x)-5*x^7+30 *x^6-47*x^5+12*x^4-18*x^3)/((x^8-6*x^7-x^6+30*x^5+25*x^4)*ln(x)^2+((-2*x^7 +12*x^6-8*x^5-30*x^4)*exp(x)-10*x^7+60*x^6-44*x^5-126*x^4-16*x^3-60*x^2)*l n(x)+(x^6-6*x^5+9*x^4)*exp(x)^2+(10*x^6-60*x^5+94*x^4-24*x^3+36*x^2)*exp(x )+25*x^6-150*x^5+245*x^4-120*x^3+184*x^2-24*x+36),x)
Output:
x^2*(-3+x)/(x^2-3*x-5)+x^2*(exp(x)*x^4+5*x^4-6*exp(x)*x^3-30*x^3+9*exp(x)* x^2+47*x^2-12*x+18)/(x^2-3*x-5)/(x^4*ln(x)-exp(x)*x^3-3*x^3*ln(x)-5*x^3+3* exp(x)*x^2-5*x^2*ln(x)+15*x^2-2*x+6)
Time = 0.10 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.82 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\frac {{\left (x^{5} - 3 \, x^{4}\right )} \log \left (x\right )}{5 \, x^{3} - 15 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} - {\left (x^{4} - 3 \, x^{3} - 5 \, x^{2}\right )} \log \left (x\right ) + 2 \, x - 6} \] Input:
integrate(((x^8-6*x^7-6*x^6+30*x^5)*log(x)^2+((x^8-8*x^7+21*x^6-18*x^5)*ex p(x)-10*x^7+60*x^6-98*x^5+48*x^4-72*x^3)*log(x)+(-x^7+6*x^6-9*x^5)*exp(x)- 5*x^7+30*x^6-47*x^5+12*x^4-18*x^3)/((x^8-6*x^7-x^6+30*x^5+25*x^4)*log(x)^2 +((-2*x^7+12*x^6-8*x^5-30*x^4)*exp(x)-10*x^7+60*x^6-44*x^5-126*x^4-16*x^3- 60*x^2)*log(x)+(x^6-6*x^5+9*x^4)*exp(x)^2+(10*x^6-60*x^5+94*x^4-24*x^3+36* x^2)*exp(x)+25*x^6-150*x^5+245*x^4-120*x^3+184*x^2-24*x+36),x, algorithm=" fricas")
Output:
-(x^5 - 3*x^4)*log(x)/(5*x^3 - 15*x^2 + (x^3 - 3*x^2)*e^x - (x^4 - 3*x^3 - 5*x^2)*log(x) + 2*x - 6)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.37 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.97 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {- x^{5} \log {\left (x \right )} + 3 x^{4} \log {\left (x \right )}}{- x^{4} \log {\left (x \right )} + 3 x^{3} \log {\left (x \right )} + 5 x^{3} + 5 x^{2} \log {\left (x \right )} - 15 x^{2} + 2 x + \left (x^{3} - 3 x^{2}\right ) e^{x} - 6} \] Input:
integrate(((x**8-6*x**7-6*x**6+30*x**5)*ln(x)**2+((x**8-8*x**7+21*x**6-18* x**5)*exp(x)-10*x**7+60*x**6-98*x**5+48*x**4-72*x**3)*ln(x)+(-x**7+6*x**6- 9*x**5)*exp(x)-5*x**7+30*x**6-47*x**5+12*x**4-18*x**3)/((x**8-6*x**7-x**6+ 30*x**5+25*x**4)*ln(x)**2+((-2*x**7+12*x**6-8*x**5-30*x**4)*exp(x)-10*x**7 +60*x**6-44*x**5-126*x**4-16*x**3-60*x**2)*ln(x)+(x**6-6*x**5+9*x**4)*exp( x)**2+(10*x**6-60*x**5+94*x**4-24*x**3+36*x**2)*exp(x)+25*x**6-150*x**5+24 5*x**4-120*x**3+184*x**2-24*x+36),x)
Output:
(-x**5*log(x) + 3*x**4*log(x))/(-x**4*log(x) + 3*x**3*log(x) + 5*x**3 + 5* x**2*log(x) - 15*x**2 + 2*x + (x**3 - 3*x**2)*exp(x) - 6)
Time = 0.19 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.82 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\frac {{\left (x^{5} - 3 \, x^{4}\right )} \log \left (x\right )}{5 \, x^{3} - 15 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} - {\left (x^{4} - 3 \, x^{3} - 5 \, x^{2}\right )} \log \left (x\right ) + 2 \, x - 6} \] Input:
integrate(((x^8-6*x^7-6*x^6+30*x^5)*log(x)^2+((x^8-8*x^7+21*x^6-18*x^5)*ex p(x)-10*x^7+60*x^6-98*x^5+48*x^4-72*x^3)*log(x)+(-x^7+6*x^6-9*x^5)*exp(x)- 5*x^7+30*x^6-47*x^5+12*x^4-18*x^3)/((x^8-6*x^7-x^6+30*x^5+25*x^4)*log(x)^2 +((-2*x^7+12*x^6-8*x^5-30*x^4)*exp(x)-10*x^7+60*x^6-44*x^5-126*x^4-16*x^3- 60*x^2)*log(x)+(x^6-6*x^5+9*x^4)*exp(x)^2+(10*x^6-60*x^5+94*x^4-24*x^3+36* x^2)*exp(x)+25*x^6-150*x^5+245*x^4-120*x^3+184*x^2-24*x+36),x, algorithm=" maxima")
Output:
-(x^5 - 3*x^4)*log(x)/(5*x^3 - 15*x^2 + (x^3 - 3*x^2)*e^x - (x^4 - 3*x^3 - 5*x^2)*log(x) + 2*x - 6)
Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (30) = 60\).
Time = 0.25 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.27 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {x^{5} \log \left (x\right ) - 2 \, x^{4} \log \left (x\right ) - x^{3} e^{x} - 3 \, x^{3} \log \left (x\right ) - 5 \, x^{3} + 3 \, x^{2} e^{x} - 5 \, x^{2} \log \left (x\right ) + 15 \, x^{2} - 2 \, x + 6}{x^{4} \log \left (x\right ) - x^{3} e^{x} - 3 \, x^{3} \log \left (x\right ) - 5 \, x^{3} + 3 \, x^{2} e^{x} - 5 \, x^{2} \log \left (x\right ) + 15 \, x^{2} - 2 \, x + 6} \] Input:
integrate(((x^8-6*x^7-6*x^6+30*x^5)*log(x)^2+((x^8-8*x^7+21*x^6-18*x^5)*ex p(x)-10*x^7+60*x^6-98*x^5+48*x^4-72*x^3)*log(x)+(-x^7+6*x^6-9*x^5)*exp(x)- 5*x^7+30*x^6-47*x^5+12*x^4-18*x^3)/((x^8-6*x^7-x^6+30*x^5+25*x^4)*log(x)^2 +((-2*x^7+12*x^6-8*x^5-30*x^4)*exp(x)-10*x^7+60*x^6-44*x^5-126*x^4-16*x^3- 60*x^2)*log(x)+(x^6-6*x^5+9*x^4)*exp(x)^2+(10*x^6-60*x^5+94*x^4-24*x^3+36* x^2)*exp(x)+25*x^6-150*x^5+245*x^4-120*x^3+184*x^2-24*x+36),x, algorithm=" giac")
Output:
(x^5*log(x) - 2*x^4*log(x) - x^3*e^x - 3*x^3*log(x) - 5*x^3 + 3*x^2*e^x - 5*x^2*log(x) + 15*x^2 - 2*x + 6)/(x^4*log(x) - x^3*e^x - 3*x^3*log(x) - 5* x^3 + 3*x^2*e^x - 5*x^2*log(x) + 15*x^2 - 2*x + 6)
Timed out. \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=-\int \frac {\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (-x^8+8\,x^7-21\,x^6+18\,x^5\right )+72\,x^3-48\,x^4+98\,x^5-60\,x^6+10\,x^7\right )-{\ln \left (x\right )}^2\,\left (x^8-6\,x^7-6\,x^6+30\,x^5\right )+18\,x^3-12\,x^4+47\,x^5-30\,x^6+5\,x^7+{\mathrm {e}}^x\,\left (x^7-6\,x^6+9\,x^5\right )}{{\mathrm {e}}^{2\,x}\,\left (x^6-6\,x^5+9\,x^4\right )-24\,x-\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (2\,x^7-12\,x^6+8\,x^5+30\,x^4\right )+60\,x^2+16\,x^3+126\,x^4+44\,x^5-60\,x^6+10\,x^7\right )+{\mathrm {e}}^x\,\left (10\,x^6-60\,x^5+94\,x^4-24\,x^3+36\,x^2\right )+{\ln \left (x\right )}^2\,\left (x^8-6\,x^7-x^6+30\,x^5+25\,x^4\right )+184\,x^2-120\,x^3+245\,x^4-150\,x^5+25\,x^6+36} \,d x \] Input:
int(-(log(x)*(exp(x)*(18*x^5 - 21*x^6 + 8*x^7 - x^8) + 72*x^3 - 48*x^4 + 9 8*x^5 - 60*x^6 + 10*x^7) - log(x)^2*(30*x^5 - 6*x^6 - 6*x^7 + x^8) + 18*x^ 3 - 12*x^4 + 47*x^5 - 30*x^6 + 5*x^7 + exp(x)*(9*x^5 - 6*x^6 + x^7))/(exp( 2*x)*(9*x^4 - 6*x^5 + x^6) - 24*x - log(x)*(exp(x)*(30*x^4 + 8*x^5 - 12*x^ 6 + 2*x^7) + 60*x^2 + 16*x^3 + 126*x^4 + 44*x^5 - 60*x^6 + 10*x^7) + exp(x )*(36*x^2 - 24*x^3 + 94*x^4 - 60*x^5 + 10*x^6) + log(x)^2*(25*x^4 + 30*x^5 - x^6 - 6*x^7 + x^8) + 184*x^2 - 120*x^3 + 245*x^4 - 150*x^5 + 25*x^6 + 3 6),x)
Output:
-int((log(x)*(exp(x)*(18*x^5 - 21*x^6 + 8*x^7 - x^8) + 72*x^3 - 48*x^4 + 9 8*x^5 - 60*x^6 + 10*x^7) - log(x)^2*(30*x^5 - 6*x^6 - 6*x^7 + x^8) + 18*x^ 3 - 12*x^4 + 47*x^5 - 30*x^6 + 5*x^7 + exp(x)*(9*x^5 - 6*x^6 + x^7))/(exp( 2*x)*(9*x^4 - 6*x^5 + x^6) - 24*x - log(x)*(exp(x)*(30*x^4 + 8*x^5 - 12*x^ 6 + 2*x^7) + 60*x^2 + 16*x^3 + 126*x^4 + 44*x^5 - 60*x^6 + 10*x^7) + exp(x )*(36*x^2 - 24*x^3 + 94*x^4 - 60*x^5 + 10*x^6) + log(x)^2*(25*x^4 + 30*x^5 - x^6 - 6*x^7 + x^8) + 184*x^2 - 120*x^3 + 245*x^4 - 150*x^5 + 25*x^6 + 3 6), x)
Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.94 \[ \int \frac {-18 x^3+12 x^4-47 x^5+30 x^6-5 x^7+e^x \left (-9 x^5+6 x^6-x^7\right )+\left (-72 x^3+48 x^4-98 x^5+60 x^6-10 x^7+e^x \left (-18 x^5+21 x^6-8 x^7+x^8\right )\right ) \log (x)+\left (30 x^5-6 x^6-6 x^7+x^8\right ) \log ^2(x)}{36-24 x+184 x^2-120 x^3+245 x^4-150 x^5+25 x^6+e^{2 x} \left (9 x^4-6 x^5+x^6\right )+e^x \left (36 x^2-24 x^3+94 x^4-60 x^5+10 x^6\right )+\left (-60 x^2-16 x^3-126 x^4-44 x^5+60 x^6-10 x^7+e^x \left (-30 x^4-8 x^5+12 x^6-2 x^7\right )\right ) \log (x)+\left (25 x^4+30 x^5-x^6-6 x^7+x^8\right ) \log ^2(x)} \, dx=\frac {\mathrm {log}\left (x \right ) x^{4} \left (-x +3\right )}{e^{x} x^{3}-3 e^{x} x^{2}-\mathrm {log}\left (x \right ) x^{4}+3 \,\mathrm {log}\left (x \right ) x^{3}+5 \,\mathrm {log}\left (x \right ) x^{2}+5 x^{3}-15 x^{2}+2 x -6} \] Input:
int(((x^8-6*x^7-6*x^6+30*x^5)*log(x)^2+((x^8-8*x^7+21*x^6-18*x^5)*exp(x)-1 0*x^7+60*x^6-98*x^5+48*x^4-72*x^3)*log(x)+(-x^7+6*x^6-9*x^5)*exp(x)-5*x^7+ 30*x^6-47*x^5+12*x^4-18*x^3)/((x^8-6*x^7-x^6+30*x^5+25*x^4)*log(x)^2+((-2* x^7+12*x^6-8*x^5-30*x^4)*exp(x)-10*x^7+60*x^6-44*x^5-126*x^4-16*x^3-60*x^2 )*log(x)+(x^6-6*x^5+9*x^4)*exp(x)^2+(10*x^6-60*x^5+94*x^4-24*x^3+36*x^2)*e xp(x)+25*x^6-150*x^5+245*x^4-120*x^3+184*x^2-24*x+36),x)
Output:
(log(x)*x**4*( - x + 3))/(e**x*x**3 - 3*e**x*x**2 - log(x)*x**4 + 3*log(x) *x**3 + 5*log(x)*x**2 + 5*x**3 - 15*x**2 + 2*x - 6)