Integrand size = 287, antiderivative size = 32 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=x-x \left (4+\frac {1}{16} \left (e^{3 x \left (x+\frac {x}{(x-\log (x))^2}\right )}+x\right )^2\right ) \]
Leaf count is larger than twice the leaf count of optimal. \(70\) vs. \(2(32)=64\).
Time = 0.48 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.19 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=-\frac {1}{16} x \left (48+2 e^{3 x^2 \left (1+\frac {1}{(x-\log (x))^2}\right )} x+x^2+e^{\frac {6 x^2 \left (1+x^2+\log ^2(x)\right )}{(x-\log (x))^2}} x^{-\frac {12 x^3}{(x-\log (x))^2}}\right ) \]
Integrate[(48*x^3 + 3*x^5 + (-144*x^2 - 9*x^4)*Log[x] + (144*x + 9*x^3)*Lo g[x]^2 + (-48 - 3*x^2)*Log[x]^3 + E^((2*(3*x^2 + 3*x^4 - 6*x^3*Log[x] + 3* x^2*Log[x]^2))/(x^2 - 2*x*Log[x] + Log[x]^2))*(12*x^2 + x^3 + 12*x^5 + (-1 5*x^2 - 36*x^4)*Log[x] + (3*x + 36*x^3)*Log[x]^2 + (-1 - 12*x^2)*Log[x]^3) + E^((3*x^2 + 3*x^4 - 6*x^3*Log[x] + 3*x^2*Log[x]^2)/(x^2 - 2*x*Log[x] + Log[x]^2))*(12*x^3 + 4*x^4 + 12*x^6 + (-24*x^3 - 36*x^5)*Log[x] + (12*x^2 + 36*x^4)*Log[x]^2 + (-4*x - 12*x^3)*Log[x]^3))/(-16*x^3 + 48*x^2*Log[x] - 48*x*Log[x]^2 + 16*Log[x]^3),x]
-1/16*(x*(48 + 2*E^(3*x^2*(1 + (x - Log[x])^(-2)))*x + x^2 + E^((6*x^2*(1 + x^2 + Log[x]^2))/(x - Log[x])^2)/x^((12*x^3)/(x - Log[x])^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.
| \(\displaystyle \int \frac {\left (12 x^5+x^3+\left (36 x^3+3 x\right ) \log ^2(x)+12 x^2+\left (-12 x^2-1\right ) \log ^3(x)+\left (-36 x^4-15 x^2\right ) \log (x)\right ) \exp \left (\frac {2 \left (3 x^4-6 x^3 \log (x)+3 x^2+3 x^2 \log ^2(x)\right )}{x^2+\log ^2(x)-2 x \log (x)}\right )+\left (12 x^6+4 x^4+12 x^3+\left (-12 x^3-4 x\right ) \log ^3(x)+\left (-36 x^5-24 x^3\right ) \log (x)+\left (36 x^4+12 x^2\right ) \log ^2(x)\right ) \exp \left (\frac {3 x^4-6 x^3 \log (x)+3 x^2+3 x^2 \log ^2(x)}{x^2+\log ^2(x)-2 x \log (x)}\right )+3 x^5+48 x^3+\left (9 x^3+144 x\right ) \log ^2(x)+\left (-3 x^2-48\right ) \log ^3(x)+\left (-9 x^4-144 x^2\right ) \log (x)}{-16 x^3+48 x^2 \log (x)+16 \log ^3(x)-48 x \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-\left (12 x^5+x^3+\left (36 x^3+3 x\right ) \log ^2(x)+12 x^2+\left (-12 x^2-1\right ) \log ^3(x)+\left (-36 x^4-15 x^2\right ) \log (x)\right ) \exp \left (\frac {2 \left (3 x^4-6 x^3 \log (x)+3 x^2+3 x^2 \log ^2(x)\right )}{x^2+\log ^2(x)-2 x \log (x)}\right )-\left (12 x^6+4 x^4+12 x^3+\left (-12 x^3-4 x\right ) \log ^3(x)+\left (-36 x^5-24 x^3\right ) \log (x)+\left (36 x^4+12 x^2\right ) \log ^2(x)\right ) \exp \left (\frac {3 x^4-6 x^3 \log (x)+3 x^2+3 x^2 \log ^2(x)}{x^2+\log ^2(x)-2 x \log (x)}\right )-3 x^5-48 x^3-\left (9 x^3+144 x\right ) \log ^2(x)-\left (-3 x^2-48\right ) \log ^3(x)-\left (-9 x^4-144 x^2\right ) \log (x)}{16 (x-\log (x))^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{16} \int -\frac {\exp \left (\frac {6 \left (x^4+\log ^2(x) x^2+x^2\right )}{x^2-2 \log (x) x+\log ^2(x)}\right ) \left (12 x^5+x^3+12 x^2-\left (12 x^2+1\right ) \log ^3(x)+3 \left (12 x^3+x\right ) \log ^2(x)-3 \left (12 x^4+5 x^2\right ) \log (x)\right ) x^{-\frac {12 x^3}{x^2-2 \log (x) x+\log ^2(x)}}+4 \exp \left (\frac {3 \left (x^4+\log ^2(x) x^2+x^2\right )}{x^2-2 \log (x) x+\log ^2(x)}\right ) \left (3 x^6+x^4+3 x^3-\left (3 x^3+x\right ) \log ^3(x)+3 \left (3 x^4+x^2\right ) \log ^2(x)-3 \left (3 x^5+2 x^3\right ) \log (x)\right ) x^{-\frac {6 x^3}{x^2-2 \log (x) x+\log ^2(x)}}+3 x^5+48 x^3-3 \left (x^2+16\right ) \log ^3(x)+9 \left (x^3+16 x\right ) \log ^2(x)-9 \left (x^4+16 x^2\right ) \log (x)}{(x-\log (x))^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{16} \int \frac {\exp \left (\frac {6 \left (x^4+\log ^2(x) x^2+x^2\right )}{x^2-2 \log (x) x+\log ^2(x)}\right ) \left (12 x^5+x^3+12 x^2-\left (12 x^2+1\right ) \log ^3(x)+3 \left (12 x^3+x\right ) \log ^2(x)-3 \left (12 x^4+5 x^2\right ) \log (x)\right ) x^{-\frac {12 x^3}{x^2-2 \log (x) x+\log ^2(x)}}+4 \exp \left (\frac {3 \left (x^4+\log ^2(x) x^2+x^2\right )}{x^2-2 \log (x) x+\log ^2(x)}\right ) \left (3 x^6+x^4+3 x^3-\left (3 x^3+x\right ) \log ^3(x)+3 \left (3 x^4+x^2\right ) \log ^2(x)-3 \left (3 x^5+2 x^3\right ) \log (x)\right ) x^{-\frac {6 x^3}{x^2-2 \log (x) x+\log ^2(x)}}+3 x^5+48 x^3-3 \left (x^2+16\right ) \log ^3(x)+9 \left (x^3+16 x\right ) \log ^2(x)-9 \left (x^4+16 x^2\right ) \log (x)}{(x-\log (x))^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{16} \int \left (\frac {4 e^{\frac {3 x^2 \left (x^2+\log ^2(x)+1\right )}{(x-\log (x))^2}} \left (3 x^5-9 \log (x) x^4+9 \log ^2(x) x^3+x^3-3 \log ^3(x) x^2-6 \log (x) x^2+3 x^2+3 \log ^2(x) x-\log ^3(x)\right ) x^{1-\frac {6 x^3}{(x-\log (x))^2}}}{(x-\log (x))^3}+\frac {e^{\frac {6 x^2 \left (x^2+\log ^2(x)+1\right )}{(x-\log (x))^2}} \left (12 x^5-36 \log (x) x^4+36 \log ^2(x) x^3+x^3-12 \log ^3(x) x^2-15 \log (x) x^2+12 x^2+3 \log ^2(x) x-\log ^3(x)\right ) x^{-\frac {12 x^3}{(x-\log (x))^2}}}{(x-\log (x))^3}+\frac {3 x^5}{(x-\log (x))^3}+\frac {48 x^3}{(x-\log (x))^3}-\frac {9 \left (x^2+16\right ) \log (x) x^2}{(x-\log (x))^3}+\frac {9 \left (x^2+16\right ) \log ^2(x) x}{(x-\log (x))^3}-\frac {3 \left (x^2+16\right ) \log ^3(x)}{(x-\log (x))^3}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -\frac {1}{16} \int \left (\frac {4 e^{\frac {3 x^2 \left (x^2+\log ^2(x)+1\right )}{(x-\log (x))^2}} \left (3 x^5-9 \log (x) x^4+9 \log ^2(x) x^3+x^3-3 \log ^3(x) x^2-6 \log (x) x^2+3 x^2+3 \log ^2(x) x-\log ^3(x)\right ) x^{1-\frac {6 x^3}{(x-\log (x))^2}}}{(x-\log (x))^3}+\frac {e^{\frac {6 x^2 \left (x^2+\log ^2(x)+1\right )}{(x-\log (x))^2}} \left (12 x^5-36 \log (x) x^4+36 \log ^2(x) x^3+x^3-12 \log ^3(x) x^2-15 \log (x) x^2+12 x^2+3 \log ^2(x) x-\log ^3(x)\right ) x^{-\frac {12 x^3}{(x-\log (x))^2}}}{(x-\log (x))^3}+\frac {3 x^5}{(x-\log (x))^3}+\frac {48 x^3}{(x-\log (x))^3}-\frac {9 \left (x^2+16\right ) \log (x) x^2}{(x-\log (x))^3}+\frac {9 \left (x^2+16\right ) \log ^2(x) x}{(x-\log (x))^3}-\frac {3 \left (x^2+16\right ) \log ^3(x)}{(x-\log (x))^3}\right )dx\) |
Int[(48*x^3 + 3*x^5 + (-144*x^2 - 9*x^4)*Log[x] + (144*x + 9*x^3)*Log[x]^2 + (-48 - 3*x^2)*Log[x]^3 + E^((2*(3*x^2 + 3*x^4 - 6*x^3*Log[x] + 3*x^2*Lo g[x]^2))/(x^2 - 2*x*Log[x] + Log[x]^2))*(12*x^2 + x^3 + 12*x^5 + (-15*x^2 - 36*x^4)*Log[x] + (3*x + 36*x^3)*Log[x]^2 + (-1 - 12*x^2)*Log[x]^3) + E^( (3*x^2 + 3*x^4 - 6*x^3*Log[x] + 3*x^2*Log[x]^2)/(x^2 - 2*x*Log[x] + Log[x] ^2))*(12*x^3 + 4*x^4 + 12*x^6 + (-24*x^3 - 36*x^5)*Log[x] + (12*x^2 + 36*x ^4)*Log[x]^2 + (-4*x - 12*x^3)*Log[x]^3))/(-16*x^3 + 48*x^2*Log[x] - 48*x* Log[x]^2 + 16*Log[x]^3),x]
3.18.78.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(73\) vs. \(2(29)=58\).
Time = 3.16 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.31
| method | result | size |
| risch | \(-\frac {x^{3}}{16}-3 x -\frac {x \,{\mathrm e}^{\frac {6 x^{2} \left (\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+1\right )}{\left (\ln \left (x \right )-x \right )^{2}}}}{16}-\frac {x^{2} {\mathrm e}^{\frac {3 x^{2} \left (\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+1\right )}{\left (\ln \left (x \right )-x \right )^{2}}}}{8}\) | \(74\) |
| parallelrisch | \(-\frac {x^{3}}{16}-3 x -\frac {x \,{\mathrm e}^{\frac {6 x^{2} \ln \left (x \right )^{2}-12 x^{3} \ln \left (x \right )+6 x^{4}+6 x^{2}}{\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}}}}{16}-\frac {x^{2} {\mathrm e}^{\frac {3 x^{2} \ln \left (x \right )^{2}-6 x^{3} \ln \left (x \right )+3 x^{4}+3 x^{2}}{\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}}}}{8}\) | \(108\) |
int((((-12*x^2-1)*ln(x)^3+(36*x^3+3*x)*ln(x)^2+(-36*x^4-15*x^2)*ln(x)+12*x ^5+x^3+12*x^2)*exp((3*x^2*ln(x)^2-6*x^3*ln(x)+3*x^4+3*x^2)/(ln(x)^2-2*x*ln (x)+x^2))^2+((-12*x^3-4*x)*ln(x)^3+(36*x^4+12*x^2)*ln(x)^2+(-36*x^5-24*x^3 )*ln(x)+12*x^6+4*x^4+12*x^3)*exp((3*x^2*ln(x)^2-6*x^3*ln(x)+3*x^4+3*x^2)/( ln(x)^2-2*x*ln(x)+x^2))+(-3*x^2-48)*ln(x)^3+(9*x^3+144*x)*ln(x)^2+(-9*x^4- 144*x^2)*ln(x)+3*x^5+48*x^3)/(16*ln(x)^3-48*x*ln(x)^2+48*x^2*ln(x)-16*x^3) ,x,method=_RETURNVERBOSE)
-1/16*x^3-3*x-1/16*x*exp(6*x^2*(ln(x)^2-2*x*ln(x)+x^2+1)/(ln(x)-x)^2)-1/8* x^2*exp(3*x^2*(ln(x)^2-2*x*ln(x)+x^2+1)/(ln(x)-x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.03 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=-\frac {1}{16} \, x^{3} - \frac {1}{8} \, x^{2} e^{\left (\frac {3 \, {\left (x^{4} - 2 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + x^{2}\right )}}{x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}}\right )} - \frac {1}{16} \, x e^{\left (\frac {6 \, {\left (x^{4} - 2 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + x^{2}\right )}}{x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}}\right )} - 3 \, x \]
integrate((((-12*x^2-1)*log(x)^3+(36*x^3+3*x)*log(x)^2+(-36*x^4-15*x^2)*lo g(x)+12*x^5+x^3+12*x^2)*exp((3*x^2*log(x)^2-6*x^3*log(x)+3*x^4+3*x^2)/(log (x)^2-2*x*log(x)+x^2))^2+((-12*x^3-4*x)*log(x)^3+(36*x^4+12*x^2)*log(x)^2+ (-36*x^5-24*x^3)*log(x)+12*x^6+4*x^4+12*x^3)*exp((3*x^2*log(x)^2-6*x^3*log (x)+3*x^4+3*x^2)/(log(x)^2-2*x*log(x)+x^2))+(-3*x^2-48)*log(x)^3+(9*x^3+14 4*x)*log(x)^2+(-9*x^4-144*x^2)*log(x)+3*x^5+48*x^3)/(16*log(x)^3-48*x*log( x)^2+48*x^2*log(x)-16*x^3),x, algorithm=\
-1/16*x^3 - 1/8*x^2*e^(3*(x^4 - 2*x^3*log(x) + x^2*log(x)^2 + x^2)/(x^2 - 2*x*log(x) + log(x)^2)) - 1/16*x*e^(6*(x^4 - 2*x^3*log(x) + x^2*log(x)^2 + x^2)/(x^2 - 2*x*log(x) + log(x)^2)) - 3*x
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (24) = 48\).
Time = 48.17 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.41 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=- \frac {x^{3}}{16} - \frac {x^{2} e^{\frac {3 x^{4} - 6 x^{3} \log {\left (x \right )} + 3 x^{2} \log {\left (x \right )}^{2} + 3 x^{2}}{x^{2} - 2 x \log {\left (x \right )} + \log {\left (x \right )}^{2}}}}{8} - \frac {x e^{\frac {2 \cdot \left (3 x^{4} - 6 x^{3} \log {\left (x \right )} + 3 x^{2} \log {\left (x \right )}^{2} + 3 x^{2}\right )}{x^{2} - 2 x \log {\left (x \right )} + \log {\left (x \right )}^{2}}}}{16} - 3 x \]
integrate((((-12*x**2-1)*ln(x)**3+(36*x**3+3*x)*ln(x)**2+(-36*x**4-15*x**2 )*ln(x)+12*x**5+x**3+12*x**2)*exp((3*x**2*ln(x)**2-6*x**3*ln(x)+3*x**4+3*x **2)/(ln(x)**2-2*x*ln(x)+x**2))**2+((-12*x**3-4*x)*ln(x)**3+(36*x**4+12*x* *2)*ln(x)**2+(-36*x**5-24*x**3)*ln(x)+12*x**6+4*x**4+12*x**3)*exp((3*x**2* ln(x)**2-6*x**3*ln(x)+3*x**4+3*x**2)/(ln(x)**2-2*x*ln(x)+x**2))+(-3*x**2-4 8)*ln(x)**3+(9*x**3+144*x)*ln(x)**2+(-9*x**4-144*x**2)*ln(x)+3*x**5+48*x** 3)/(16*ln(x)**3-48*x*ln(x)**2+48*x**2*ln(x)-16*x**3),x)
-x**3/16 - x**2*exp((3*x**4 - 6*x**3*log(x) + 3*x**2*log(x)**2 + 3*x**2)/( x**2 - 2*x*log(x) + log(x)**2))/8 - x*exp(2*(3*x**4 - 6*x**3*log(x) + 3*x* *2*log(x)**2 + 3*x**2)/(x**2 - 2*x*log(x) + log(x)**2))/16 - 3*x
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.56 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=-\frac {1}{16} \, {\left (2 \, x^{2} e^{\left (3 \, x^{2} + \frac {3 \, \log \left (x\right )^{2}}{x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {6 \, \log \left (x\right )}{x - \log \left (x\right )} + 3\right )} + x e^{\left (6 \, x^{2} + \frac {6 \, \log \left (x\right )^{2}}{x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}} + 6\right )} + \frac {x^{3} + 48 \, x}{x^{\frac {12}{x - \log \left (x\right )}}}\right )} x^{\frac {12}{x - \log \left (x\right )}} \]
integrate((((-12*x^2-1)*log(x)^3+(36*x^3+3*x)*log(x)^2+(-36*x^4-15*x^2)*lo g(x)+12*x^5+x^3+12*x^2)*exp((3*x^2*log(x)^2-6*x^3*log(x)+3*x^4+3*x^2)/(log (x)^2-2*x*log(x)+x^2))^2+((-12*x^3-4*x)*log(x)^3+(36*x^4+12*x^2)*log(x)^2+ (-36*x^5-24*x^3)*log(x)+12*x^6+4*x^4+12*x^3)*exp((3*x^2*log(x)^2-6*x^3*log (x)+3*x^4+3*x^2)/(log(x)^2-2*x*log(x)+x^2))+(-3*x^2-48)*log(x)^3+(9*x^3+14 4*x)*log(x)^2+(-9*x^4-144*x^2)*log(x)+3*x^5+48*x^3)/(16*log(x)^3-48*x*log( x)^2+48*x^2*log(x)-16*x^3),x, algorithm=\
-1/16*(2*x^2*e^(3*x^2 + 3*log(x)^2/(x^2 - 2*x*log(x) + log(x)^2) - 6*log(x )/(x - log(x)) + 3) + x*e^(6*x^2 + 6*log(x)^2/(x^2 - 2*x*log(x) + log(x)^2 ) + 6) + (x^3 + 48*x)/x^(12/(x - log(x))))*x^(12/(x - log(x)))
Exception generated. \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=\text {Exception raised: TypeError} \]
integrate((((-12*x^2-1)*log(x)^3+(36*x^3+3*x)*log(x)^2+(-36*x^4-15*x^2)*lo g(x)+12*x^5+x^3+12*x^2)*exp((3*x^2*log(x)^2-6*x^3*log(x)+3*x^4+3*x^2)/(log (x)^2-2*x*log(x)+x^2))^2+((-12*x^3-4*x)*log(x)^3+(36*x^4+12*x^2)*log(x)^2+ (-36*x^5-24*x^3)*log(x)+12*x^6+4*x^4+12*x^3)*exp((3*x^2*log(x)^2-6*x^3*log (x)+3*x^4+3*x^2)/(log(x)^2-2*x*log(x)+x^2))+(-3*x^2-48)*log(x)^3+(9*x^3+14 4*x)*log(x)^2+(-9*x^4-144*x^2)*log(x)+3*x^5+48*x^3)/(16*log(x)^3-48*x*log( x)^2+48*x^2*log(x)-16*x^3),x, algorithm=\
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro unding error%%%{62208,[2,38]%%%}+%%%{-808704,[2,37]%%%}+%%%{4852224,[2,36] %%%}+%%%{
Time = 13.15 (sec) , antiderivative size = 197, normalized size of antiderivative = 6.16 \[ \int \frac {48 x^3+3 x^5+\left (-144 x^2-9 x^4\right ) \log (x)+\left (144 x+9 x^3\right ) \log ^2(x)+\left (-48-3 x^2\right ) \log ^3(x)+e^{\frac {2 \left (3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)\right )}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^2+x^3+12 x^5+\left (-15 x^2-36 x^4\right ) \log (x)+\left (3 x+36 x^3\right ) \log ^2(x)+\left (-1-12 x^2\right ) \log ^3(x)\right )+e^{\frac {3 x^2+3 x^4-6 x^3 \log (x)+3 x^2 \log ^2(x)}{x^2-2 x \log (x)+\log ^2(x)}} \left (12 x^3+4 x^4+12 x^6+\left (-24 x^3-36 x^5\right ) \log (x)+\left (12 x^2+36 x^4\right ) \log ^2(x)+\left (-4 x-12 x^3\right ) \log ^3(x)\right )}{-16 x^3+48 x^2 \log (x)-48 x \log ^2(x)+16 \log ^3(x)} \, dx=-3\,x-\frac {x^3}{16}-\frac {x^2\,{\mathrm {e}}^{\frac {3\,x^2}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}+\frac {3\,x^4}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}+\frac {3\,x^2\,{\ln \left (x\right )}^2}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}}}{8\,x^{\frac {6\,x^3}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}}}-\frac {x\,{\mathrm {e}}^{\frac {6\,x^2}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}+\frac {6\,x^4}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}+\frac {6\,x^2\,{\ln \left (x\right )}^2}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}}}{16\,x^{\frac {12\,x^3}{x^2-2\,x\,\ln \left (x\right )+{\ln \left (x\right )}^2}}} \]
int(-(log(x)^2*(144*x + 9*x^3) - log(x)*(144*x^2 + 9*x^4) + exp((2*(3*x^2* log(x)^2 - 6*x^3*log(x) + 3*x^2 + 3*x^4))/(log(x)^2 - 2*x*log(x) + x^2))*( log(x)^2*(3*x + 36*x^3) - log(x)*(15*x^2 + 36*x^4) - log(x)^3*(12*x^2 + 1) + 12*x^2 + x^3 + 12*x^5) - log(x)^3*(3*x^2 + 48) + exp((3*x^2*log(x)^2 - 6*x^3*log(x) + 3*x^2 + 3*x^4)/(log(x)^2 - 2*x*log(x) + x^2))*(log(x)^2*(12 *x^2 + 36*x^4) - log(x)*(24*x^3 + 36*x^5) - log(x)^3*(4*x + 12*x^3) + 12*x ^3 + 4*x^4 + 12*x^6) + 48*x^3 + 3*x^5)/(48*x*log(x)^2 - 48*x^2*log(x) - 16 *log(x)^3 + 16*x^3),x)
- 3*x - x^3/16 - (x^2*exp((3*x^2)/(log(x)^2 - 2*x*log(x) + x^2) + (3*x^4)/ (log(x)^2 - 2*x*log(x) + x^2) + (3*x^2*log(x)^2)/(log(x)^2 - 2*x*log(x) + x^2)))/(8*x^((6*x^3)/(log(x)^2 - 2*x*log(x) + x^2))) - (x*exp((6*x^2)/(log (x)^2 - 2*x*log(x) + x^2) + (6*x^4)/(log(x)^2 - 2*x*log(x) + x^2) + (6*x^2 *log(x)^2)/(log(x)^2 - 2*x*log(x) + x^2)))/(16*x^((12*x^3)/(log(x)^2 - 2*x *log(x) + x^2)))