Integrand size = 347, antiderivative size = 35 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\frac {\left (-e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}}+x+\log (3+x)\right )^2}{-1-x} \] Output:
(x-exp(3/x^2/ln(x^2-x)^2)+ln(3+x))^2/(-1-x)
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(35)=70\).
Time = 0.24 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.20 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=-\frac {1+e^{\frac {6}{x^2 \log ^2((-1+x) x)}}+x-2 e^{\frac {3}{x^2 \log ^2((-1+x) x)}} x+x^2-2 \left (e^{\frac {3}{x^2 \log ^2((-1+x) x)}}-x\right ) \log (3+x)+\log ^2(3+x)}{1+x} \] Input:
Integrate[((8*x^4 - x^5 - 6*x^6 - x^7 + (8*x^3 - 4*x^4 - 4*x^5)*Log[3 + x] + (-3*x^3 + 2*x^4 + x^5)*Log[3 + x]^2)*Log[-x + x^2]^3 + E^(6/(x^2*Log[-x + x^2]^2))*(-36 + 24*x + 84*x^2 + 24*x^3 + (-36 - 12*x + 36*x^2 + 12*x^3) *Log[-x + x^2] + (-3*x^3 + 2*x^4 + x^5)*Log[-x + x^2]^3) + E^(3/(x^2*Log[- x + x^2]^2))*(36*x - 24*x^2 - 84*x^3 - 24*x^4 + (36 - 24*x - 84*x^2 - 24*x ^3)*Log[3 + x] + (36*x + 12*x^2 - 36*x^3 - 12*x^4 + (36 + 12*x - 36*x^2 - 12*x^3)*Log[3 + x])*Log[-x + x^2] + (-8*x^3 + 4*x^4 + 4*x^5 + (6*x^3 - 4*x ^4 - 2*x^5)*Log[3 + x])*Log[-x + x^2]^3))/((-3*x^3 - 4*x^4 + 2*x^5 + 4*x^6 + x^7)*Log[-x + x^2]^3),x]
Output:
-((1 + E^(6/(x^2*Log[(-1 + x)*x]^2)) + x - 2*E^(3/(x^2*Log[(-1 + x)*x]^2)) *x + x^2 - 2*(E^(3/(x^2*Log[(-1 + x)*x]^2)) - x)*Log[3 + x] + Log[3 + x]^2 )/(1 + 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.
| \(\displaystyle \int \frac {e^{\frac {6}{x^2 \log ^2\left (x^2-x\right )}} \left (24 x^3+84 x^2+\left (12 x^3+36 x^2-12 x-36\right ) \log \left (x^2-x\right )+\left (x^5+2 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )+24 x-36\right )+e^{\frac {3}{x^2 \log ^2\left (x^2-x\right )}} \left (-24 x^4-84 x^3-24 x^2+\left (-24 x^3-84 x^2-24 x+36\right ) \log (x+3)+\left (-12 x^4-36 x^3+12 x^2+\left (-12 x^3-36 x^2+12 x+36\right ) \log (x+3)+36 x\right ) \log \left (x^2-x\right )+\left (4 x^5+4 x^4-8 x^3+\left (-2 x^5-4 x^4+6 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+36 x\right )+\left (-x^7-6 x^6-x^5+8 x^4+\left (x^5+2 x^4-3 x^3\right ) \log ^2(x+3)+\left (-4 x^5-4 x^4+8 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )}{\left (x^7+4 x^6+2 x^5-4 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^{\frac {6}{x^2 \log ^2\left (x^2-x\right )}} \left (24 x^3+84 x^2+\left (12 x^3+36 x^2-12 x-36\right ) \log \left (x^2-x\right )+\left (x^5+2 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )+24 x-36\right )+e^{\frac {3}{x^2 \log ^2\left (x^2-x\right )}} \left (-24 x^4-84 x^3-24 x^2+\left (-24 x^3-84 x^2-24 x+36\right ) \log (x+3)+\left (-12 x^4-36 x^3+12 x^2+\left (-12 x^3-36 x^2+12 x+36\right ) \log (x+3)+36 x\right ) \log \left (x^2-x\right )+\left (4 x^5+4 x^4-8 x^3+\left (-2 x^5-4 x^4+6 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+36 x\right )+\left (-x^7-6 x^6-x^5+8 x^4+\left (x^5+2 x^4-3 x^3\right ) \log ^2(x+3)+\left (-4 x^5-4 x^4+8 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )}{x^3 \left (x^4+4 x^3+2 x^2-4 x-3\right ) \log ^3\left (x^2-x\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (-\frac {\left (-x^7-6 x^6-x^5+8 x^4+\left (x^5+2 x^4-3 x^3\right ) \log ^2(x+3)+\left (-4 x^5-4 x^4+8 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+e^{\frac {6}{x^2 \log ^2\left (x^2-x\right )}} \left (24 x^3+84 x^2+24 x+\left (x^5+2 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )+\left (12 x^3+36 x^2-12 x-36\right ) \log \left (x^2-x\right )-36\right )+e^{\frac {3}{x^2 \log ^2\left (x^2-x\right )}} \left (-24 x^4-84 x^3-24 x^2+36 x+\left (4 x^5+4 x^4-8 x^3+\left (-2 x^5-4 x^4+6 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+\left (-24 x^3-84 x^2-24 x+36\right ) \log (x+3)+\left (-12 x^4-36 x^3+12 x^2+36 x+\left (-12 x^3-36 x^2+12 x+36\right ) \log (x+3)\right ) \log \left (x^2-x\right )\right )}{16 x^3 (x+3) \log ^3\left (x^2-x\right )}-\frac {\left (-x^7-6 x^6-x^5+8 x^4+\left (x^5+2 x^4-3 x^3\right ) \log ^2(x+3)+\left (-4 x^5-4 x^4+8 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+e^{\frac {6}{x^2 \log ^2\left (x^2-x\right )}} \left (24 x^3+84 x^2+24 x+\left (x^5+2 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )+\left (12 x^3+36 x^2-12 x-36\right ) \log \left (x^2-x\right )-36\right )+e^{\frac {3}{x^2 \log ^2\left (x^2-x\right )}} \left (-24 x^4-84 x^3-24 x^2+36 x+\left (4 x^5+4 x^4-8 x^3+\left (-2 x^5-4 x^4+6 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+\left (-24 x^3-84 x^2-24 x+36\right ) \log (x+3)+\left (-12 x^4-36 x^3+12 x^2+36 x+\left (-12 x^3-36 x^2+12 x+36\right ) \log (x+3)\right ) \log \left (x^2-x\right )\right )}{4 x^3 (x+1)^2 \log ^3\left (x^2-x\right )}+\frac {\left (-x^7-6 x^6-x^5+8 x^4+\left (x^5+2 x^4-3 x^3\right ) \log ^2(x+3)+\left (-4 x^5-4 x^4+8 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+e^{\frac {6}{x^2 \log ^2\left (x^2-x\right )}} \left (24 x^3+84 x^2+24 x+\left (x^5+2 x^4-3 x^3\right ) \log ^3\left (x^2-x\right )+\left (12 x^3+36 x^2-12 x-36\right ) \log \left (x^2-x\right )-36\right )+e^{\frac {3}{x^2 \log ^2\left (x^2-x\right )}} \left (-24 x^4-84 x^3-24 x^2+36 x+\left (4 x^5+4 x^4-8 x^3+\left (-2 x^5-4 x^4+6 x^3\right ) \log (x+3)\right ) \log ^3\left (x^2-x\right )+\left (-24 x^3-84 x^2-24 x+36\right ) \log (x+3)+\left (-12 x^4-36 x^3+12 x^2+36 x+\left (-12 x^3-36 x^2+12 x+36\right ) \log (x+3)\right ) \log \left (x^2-x\right )\right )}{16 (x-1) x^3 \log ^3\left (x^2-x\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{\frac {3}{x^2 \log ^2((x-1) x)}}-x-\log (x+3)\right ) \left (-12 \left (x^3+3 x^2-x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}} \log ((x-1) x)-12 \left (2 x^3+7 x^2+2 x-3\right ) e^{\frac {3}{x^2 \log ^2((x-1) x)}}-\left ((x-1) x^3 \left (x^2+(x+3) e^{\frac {3}{x^2 \log ^2((x-1) x)}}+7 x-(x+3) \log (x+3)+8\right ) \log ^3((x-1) x)\right )\right )}{(1-x) x^3 (x+1)^2 (x+3) \log ^3((x-1) x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^3}{(x+1)^2 (x+3)}-\frac {7 x^2}{(x+1)^2 (x+3)}-\frac {x^2 \log (x+3)}{(x+1)^2 (x+3)}+\frac {e^{\frac {6}{x^2 \log ^2((x-1) x)}} \left (x^4 \log ^3((x-1) x)-x^3 \log ^3((x-1) x)+24 x^2+12 x^2 \log ((x-1) x)+12 x-12 \log ((x-1) x)-12\right )}{(x-1) (x+1)^2 x^3 \log ^3((x-1) x)}-\frac {2 e^{\frac {3}{x^2 \log ^2((x-1) x)}} \left (-2 x^5 \log ^3((x-1) x)+x^5 \log ^3((x-1) x) \log (x+3)+12 x^4-2 x^4 \log ^3((x-1) x)+2 x^4 \log ^3((x-1) x) \log (x+3)+6 x^4 \log ((x-1) x)+42 x^3+4 x^3 \log ^3((x-1) x)-3 x^3 \log ^3((x-1) x) \log (x+3)+18 x^3 \log ((x-1) x)+6 x^3 \log ((x-1) x) \log (x+3)+12 x^3 \log (x+3)+12 x^2-6 x^2 \log ((x-1) x)+18 x^2 \log ((x-1) x) \log (x+3)+42 x^2 \log (x+3)-18 x-18 x \log ((x-1) x)-6 x \log ((x-1) x) \log (x+3)+12 x \log (x+3)-18 \log ((x-1) x) \log (x+3)-18 \log (x+3)\right )}{(x-1) (x+1)^2 (x+3) x^3 \log ^3((x-1) x)}-\frac {8 x}{(x+1)^2 (x+3)}+\frac {\log ^2(x+3)}{(x+1)^2}-\frac {7 x \log (x+3)}{(x+1)^2 (x+3)}+\frac {x \log (x+3)}{(x+1)^2}-\frac {8 \log (x+3)}{(x+1)^2 (x+3)}\right )dx\) |
Input:
Int[((8*x^4 - x^5 - 6*x^6 - x^7 + (8*x^3 - 4*x^4 - 4*x^5)*Log[3 + x] + (-3 *x^3 + 2*x^4 + x^5)*Log[3 + x]^2)*Log[-x + x^2]^3 + E^(6/(x^2*Log[-x + x^2 ]^2))*(-36 + 24*x + 84*x^2 + 24*x^3 + (-36 - 12*x + 36*x^2 + 12*x^3)*Log[- x + x^2] + (-3*x^3 + 2*x^4 + x^5)*Log[-x + x^2]^3) + E^(3/(x^2*Log[-x + x^ 2]^2))*(36*x - 24*x^2 - 84*x^3 - 24*x^4 + (36 - 24*x - 84*x^2 - 24*x^3)*Lo g[3 + x] + (36*x + 12*x^2 - 36*x^3 - 12*x^4 + (36 + 12*x - 36*x^2 - 12*x^3 )*Log[3 + x])*Log[-x + x^2] + (-8*x^3 + 4*x^4 + 4*x^5 + (6*x^3 - 4*x^4 - 2 *x^5)*Log[3 + x])*Log[-x + x^2]^3))/((-3*x^3 - 4*x^4 + 2*x^5 + 4*x^6 + x^7 )*Log[-x + x^2]^3),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.04 (sec) , antiderivative size = 266, normalized size of antiderivative = 7.60
\[-\frac {\ln \left (3+x \right )^{2}}{1+x}+\frac {2 \ln \left (3+x \right )}{1+x}-\frac {2 x \ln \left (3+x \right )+x^{2}+2 \ln \left (3+x \right )+x +1}{1+x}-\frac {{\mathrm e}^{\frac {24}{x^{2} \left (-i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{3}+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )-i \pi \,\operatorname {csgn}\left (i x \left (-1+x \right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )+2 \ln \left (x \right )+2 \ln \left (-1+x \right )\right )^{2}}}}{1+x}+\frac {2 \left (x +\ln \left (3+x \right )\right ) {\mathrm e}^{\frac {12}{x^{2} \left (-i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{3}+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )-i \pi \,\operatorname {csgn}\left (i x \left (-1+x \right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )+2 \ln \left (x \right )+2 \ln \left (-1+x \right )\right )^{2}}}}{1+x}\]
Input:
int((((x^5+2*x^4-3*x^3)*ln(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*ln(x^2-x)+24*x ^3+84*x^2+24*x-36)*exp(3/x^2/ln(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*ln(3+x) +4*x^5+4*x^4-8*x^3)*ln(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*ln(3+x)-12*x^4-3 6*x^3+12*x^2+36*x)*ln(x^2-x)+(-24*x^3-84*x^2-24*x+36)*ln(3+x)-24*x^4-84*x^ 3-24*x^2+36*x)*exp(3/x^2/ln(x^2-x)^2)+((x^5+2*x^4-3*x^3)*ln(3+x)^2+(-4*x^5 -4*x^4+8*x^3)*ln(3+x)-x^7-6*x^6-x^5+8*x^4)*ln(x^2-x)^3)/(x^7+4*x^6+2*x^5-4 *x^4-3*x^3)/ln(x^2-x)^3,x)
Output:
-1/(1+x)*ln(3+x)^2+2/(1+x)*ln(3+x)-(2*x*ln(3+x)+x^2+2*ln(3+x)+x+1)/(1+x)-1 /(1+x)*exp(24/x^2/(-I*Pi*csgn(I*x*(-1+x))^3+I*Pi*csgn(I*x*(-1+x))^2*csgn(I *x)+I*Pi*csgn(I*x*(-1+x))^2*csgn(I*(-1+x))-I*Pi*csgn(I*x*(-1+x))*csgn(I*x) *csgn(I*(-1+x))+2*ln(x)+2*ln(-1+x))^2)+2*(x+ln(3+x))/(1+x)*exp(12/x^2/(-I* Pi*csgn(I*x*(-1+x))^3+I*Pi*csgn(I*x*(-1+x))^2*csgn(I*x)+I*Pi*csgn(I*x*(-1+ x))^2*csgn(I*(-1+x))-I*Pi*csgn(I*x*(-1+x))*csgn(I*x)*csgn(I*(-1+x))+2*ln(x )+2*ln(-1+x))^2)
Time = 0.08 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=-\frac {x^{2} - 2 \, {\left (x + \log \left (x + 3\right )\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} + x + e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 1}{x + 1} \] Input:
integrate((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2 -x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3 )*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log(3 +x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x )-24*x^4-84*x^3-24*x^2+36*x)*exp(3/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*lo g(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)^3)/ (x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="fricas")
Output:
-(x^2 - 2*(x + log(x + 3))*e^(3/(x^2*log(x^2 - x)^2)) + 2*x*log(x + 3) + l og(x + 3)^2 + x + e^(6/(x^2*log(x^2 - x)^2)) + 1)/(x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.68 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.86 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=- x + \frac {\left (- x - 1\right ) e^{\frac {6}{x^{2} \log {\left (x^{2} - x \right )}^{2}}} + \left (2 x^{2} + 2 x \log {\left (x + 3 \right )} + 2 x + 2 \log {\left (x + 3 \right )}\right ) e^{\frac {3}{x^{2} \log {\left (x^{2} - x \right )}^{2}}}}{x^{2} + 2 x + 1} - 2 \log {\left (x + 3 \right )} - \frac {\log {\left (x + 3 \right )}^{2}}{x + 1} + \frac {2 \log {\left (x + 3 \right )}}{x + 1} - \frac {1}{x + 1} \] Input:
integrate((((x**5+2*x**4-3*x**3)*ln(x**2-x)**3+(12*x**3+36*x**2-12*x-36)*l n(x**2-x)+24*x**3+84*x**2+24*x-36)*exp(3/x**2/ln(x**2-x)**2)**2+(((-2*x**5 -4*x**4+6*x**3)*ln(3+x)+4*x**5+4*x**4-8*x**3)*ln(x**2-x)**3+((-12*x**3-36* x**2+12*x+36)*ln(3+x)-12*x**4-36*x**3+12*x**2+36*x)*ln(x**2-x)+(-24*x**3-8 4*x**2-24*x+36)*ln(3+x)-24*x**4-84*x**3-24*x**2+36*x)*exp(3/x**2/ln(x**2-x )**2)+((x**5+2*x**4-3*x**3)*ln(3+x)**2+(-4*x**5-4*x**4+8*x**3)*ln(3+x)-x** 7-6*x**6-x**5+8*x**4)*ln(x**2-x)**3)/(x**7+4*x**6+2*x**5-4*x**4-3*x**3)/ln (x**2-x)**3,x)
Output:
-x + ((-x - 1)*exp(6/(x**2*log(x**2 - x)**2)) + (2*x**2 + 2*x*log(x + 3) + 2*x + 2*log(x + 3))*exp(3/(x**2*log(x**2 - x)**2)))/(x**2 + 2*x + 1) - 2* log(x + 3) - log(x + 3)**2/(x + 1) + 2*log(x + 3)/(x + 1) - 1/(x + 1)
\[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int { -\frac {{\left (x^{7} + 6 \, x^{6} + x^{5} - 8 \, x^{4} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )^{2} + 4 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} - {\left ({\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3} + 24 \, x^{3} + 84 \, x^{2} + 12 \, {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x^{2} - x\right ) + 24 \, x - 36\right )} e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, {\left (12 \, x^{4} - {\left (2 \, x^{5} + 2 \, x^{4} - 4 \, x^{3} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} + 42 \, x^{3} + 12 \, x^{2} + 6 \, {\left (x^{4} + 3 \, x^{3} - x^{2} + {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x + 3\right ) - 3 \, x\right )} \log \left (x^{2} - x\right ) + 6 \, {\left (2 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} \log \left (x + 3\right ) - 18 \, x\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )}}{{\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3}} \,d x } \] Input:
integrate((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2 -x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3 )*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log(3 +x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x )-24*x^4-84*x^3-24*x^2+36*x)*exp(3/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*lo g(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)^3)/ (x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="maxima")
Output:
-(x^2 + 2*x*log(x + 3) + log(x + 3)^2 + x + 1)/(x + 1) + integrate(((x^4 - x^3)*log(x - 1)^3 + 3*(x^4 - x^3)*log(x - 1)^2*log(x) + (x^4 - x^3)*log(x )^3 + 24*x^2 + 3*((x^4 - x^3)*log(x)^2 + 4*x^2 - 4)*log(x - 1) + 12*(x^2 - 1)*log(x) + 12*x - 12)*e^(6/(x^2*log(x - 1)^2 + 2*x^2*log(x - 1)*log(x) + x^2*log(x)^2))/((x^6 + x^5 - x^4 - x^3)*log(x - 1)^3 + 3*(x^6 + x^5 - x^4 - x^3)*log(x - 1)^2*log(x) + 3*(x^6 + x^5 - x^4 - x^3)*log(x - 1)*log(x)^ 2 + (x^6 + x^5 - x^4 - x^3)*log(x)^3), x) - integrate(2*(12*x^4 - 2*(x^5 + x^4 - 2*x^3)*log(x - 1)^3 - 6*(x^5 + x^4 - 2*x^3)*log(x - 1)^2*log(x) - 2 *(x^5 + x^4 - 2*x^3)*log(x)^3 + 42*x^3 + 12*x^2 + ((x^5 + 2*x^4 - 3*x^3)*l og(x - 1)^3 + 3*(x^5 + 2*x^4 - 3*x^3)*log(x - 1)^2*log(x) + (x^5 + 2*x^4 - 3*x^3)*log(x)^3 + 12*x^3 + 42*x^2 + 3*(2*x^3 + (x^5 + 2*x^4 - 3*x^3)*log( x)^2 + 6*x^2 - 2*x - 6)*log(x - 1) + 6*(x^3 + 3*x^2 - x - 3)*log(x) + 12*x - 18)*log(x + 3) + 6*(x^4 + 3*x^3 - (x^5 + x^4 - 2*x^3)*log(x)^2 - x^2 - 3*x)*log(x - 1) + 6*(x^4 + 3*x^3 - x^2 - 3*x)*log(x) - 18*x)*e^(3/(x^2*log (x - 1)^2 + 2*x^2*log(x - 1)*log(x) + x^2*log(x)^2))/((x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x - 1)^3 + 3*(x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*l og(x - 1)^2*log(x) + 3*(x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x - 1)*lo g(x)^2 + (x^7 + 4*x^6 + 2*x^5 - 4*x^4 - 3*x^3)*log(x)^3), x)
\[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int { -\frac {{\left (x^{7} + 6 \, x^{6} + x^{5} - 8 \, x^{4} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )^{2} + 4 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} - {\left ({\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3} + 24 \, x^{3} + 84 \, x^{2} + 12 \, {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x^{2} - x\right ) + 24 \, x - 36\right )} e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, {\left (12 \, x^{4} - {\left (2 \, x^{5} + 2 \, x^{4} - 4 \, x^{3} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} + 42 \, x^{3} + 12 \, x^{2} + 6 \, {\left (x^{4} + 3 \, x^{3} - x^{2} + {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x + 3\right ) - 3 \, x\right )} \log \left (x^{2} - x\right ) + 6 \, {\left (2 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} \log \left (x + 3\right ) - 18 \, x\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )}}{{\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3}} \,d x } \] Input:
integrate((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2 -x)+24*x^3+84*x^2+24*x-36)*exp(3/x^2/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3 )*log(3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log(3 +x)-12*x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x )-24*x^4-84*x^3-24*x^2+36*x)*exp(3/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*lo g(3+x)^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)^3)/ (x^7+4*x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x, algorithm="giac")
Output:
undef
Timed out. \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int -\frac {{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (4\,x^5+4\,x^4-8\,x^3\right )-{\ln \left (x+3\right )}^2\,\left (x^5+2\,x^4-3\,x^3\right )-8\,x^4+x^5+6\,x^6+x^7\right )-{\mathrm {e}}^{\frac {6}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (24\,x-\ln \left (x^2-x\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+84\,x^2+24\,x^3+{\ln \left (x^2-x\right )}^3\,\left (x^5+2\,x^4-3\,x^3\right )-36\right )+{\mathrm {e}}^{\frac {3}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (\ln \left (x+3\right )\,\left (24\,x^3+84\,x^2+24\,x-36\right )-36\,x+24\,x^2+84\,x^3+24\,x^4+{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (2\,x^5+4\,x^4-6\,x^3\right )+8\,x^3-4\,x^4-4\,x^5\right )-\ln \left (x^2-x\right )\,\left (36\,x+\ln \left (x+3\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+12\,x^2-36\,x^3-12\,x^4\right )\right )}{{\ln \left (x^2-x\right )}^3\,\left (x^7+4\,x^6+2\,x^5-4\,x^4-3\,x^3\right )} \,d x \] Input:
int(-(log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 8*x^3 + 4*x^5) - log(x + 3)^2*(2 *x^4 - 3*x^3 + x^5) - 8*x^4 + x^5 + 6*x^6 + x^7) - exp(6/(x^2*log(x^2 - x) ^2))*(24*x - log(x^2 - x)*(12*x - 36*x^2 - 12*x^3 + 36) + 84*x^2 + 24*x^3 + log(x^2 - x)^3*(2*x^4 - 3*x^3 + x^5) - 36) + exp(3/(x^2*log(x^2 - x)^2)) *(log(x + 3)*(24*x + 84*x^2 + 24*x^3 - 36) - 36*x + 24*x^2 + 84*x^3 + 24*x ^4 + log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 6*x^3 + 2*x^5) + 8*x^3 - 4*x^4 - 4*x^5) - log(x^2 - x)*(36*x + log(x + 3)*(12*x - 36*x^2 - 12*x^3 + 36) + 1 2*x^2 - 36*x^3 - 12*x^4)))/(log(x^2 - x)^3*(2*x^5 - 4*x^4 - 3*x^3 + 4*x^6 + x^7)),x)
Output:
int(-(log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 8*x^3 + 4*x^5) - log(x + 3)^2*(2 *x^4 - 3*x^3 + x^5) - 8*x^4 + x^5 + 6*x^6 + x^7) - exp(6/(x^2*log(x^2 - x) ^2))*(24*x - log(x^2 - x)*(12*x - 36*x^2 - 12*x^3 + 36) + 84*x^2 + 24*x^3 + log(x^2 - x)^3*(2*x^4 - 3*x^3 + x^5) - 36) + exp(3/(x^2*log(x^2 - x)^2)) *(log(x + 3)*(24*x + 84*x^2 + 24*x^3 - 36) - 36*x + 24*x^2 + 84*x^3 + 24*x ^4 + log(x^2 - x)^3*(log(x + 3)*(4*x^4 - 6*x^3 + 2*x^5) + 8*x^3 - 4*x^4 - 4*x^5) - log(x^2 - x)*(36*x + log(x + 3)*(12*x - 36*x^2 - 12*x^3 + 36) + 1 2*x^2 - 36*x^3 - 12*x^4)))/(log(x^2 - x)^3*(2*x^5 - 4*x^4 - 3*x^3 + 4*x^6 + x^7)), x)
Time = 0.19 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.54 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\frac {-e^{\frac {6}{\mathrm {log}\left (x^{2}-x \right )^{2} x^{2}}}+2 e^{\frac {3}{\mathrm {log}\left (x^{2}-x \right )^{2} x^{2}}} \mathrm {log}\left (x +3\right )+2 e^{\frac {3}{\mathrm {log}\left (x^{2}-x \right )^{2} x^{2}}} x -\mathrm {log}\left (x +3\right )^{2}-2 \,\mathrm {log}\left (x +3\right ) x -x^{2}}{x +1} \] Input:
int((((x^5+2*x^4-3*x^3)*log(x^2-x)^3+(12*x^3+36*x^2-12*x-36)*log(x^2-x)+24 *x^3+84*x^2+24*x-36)*exp(3/x^2/log(x^2-x)^2)^2+(((-2*x^5-4*x^4+6*x^3)*log( 3+x)+4*x^5+4*x^4-8*x^3)*log(x^2-x)^3+((-12*x^3-36*x^2+12*x+36)*log(3+x)-12 *x^4-36*x^3+12*x^2+36*x)*log(x^2-x)+(-24*x^3-84*x^2-24*x+36)*log(3+x)-24*x ^4-84*x^3-24*x^2+36*x)*exp(3/x^2/log(x^2-x)^2)+((x^5+2*x^4-3*x^3)*log(3+x) ^2+(-4*x^5-4*x^4+8*x^3)*log(3+x)-x^7-6*x^6-x^5+8*x^4)*log(x^2-x)^3)/(x^7+4 *x^6+2*x^5-4*x^4-3*x^3)/log(x^2-x)^3,x)
Output:
( - e**(6/(log(x**2 - x)**2*x**2)) + 2*e**(3/(log(x**2 - x)**2*x**2))*log( x + 3) + 2*e**(3/(log(x**2 - x)**2*x**2))*x - log(x + 3)**2 - 2*log(x + 3) *x - x**2)/(x + 1)