Integrand size = 258, antiderivative size = 35 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=e^{\left (-x^2+(2-x) x^2-\frac {x}{2 x-\frac {\log (x)}{x}}\right )^2} \]
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(35)=70\).
Time = 0.38 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.20 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=e^{\frac {x^4 \left (\left (1-2 x^2+2 x^3\right )^2+(-1+x)^2 \log ^2(x)\right )}{\left (-2 x^2+\log (x)\right )^2}} x^{-\frac {2 x^4 \left (-1+x+2 x^2-4 x^3+2 x^4\right )}{\left (-2 x^2+\log (x)\right )^2}} \]
Integrate[(E^((x^4 - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + (2*x^4 - 2*x ^5 - 4*x^6 + 8*x^7 - 4*x^8)*Log[x] + (x^4 - 2*x^5 + x^6)*Log[x]^2)/(4*x^4 - 4*x^2*Log[x] + Log[x]^2))*(-2*x^3 + 4*x^5 - 4*x^6 + 16*x^7 - 24*x^8 - 32 *x^9 + 80*x^10 - 48*x^11 + (2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120 *x^8 + 72*x^9)*Log[x] + (8*x^3 - 10*x^4 - 24*x^5 + 60*x^6 - 36*x^7)*Log[x] ^2 + (4*x^3 - 10*x^4 + 6*x^5)*Log[x]^3))/(-8*x^6 + 12*x^4*Log[x] - 6*x^2*L og[x]^2 + Log[x]^3),x]
E^((x^4*((1 - 2*x^2 + 2*x^3)^2 + (-1 + x)^2*Log[x]^2))/(-2*x^2 + Log[x])^2 )/x^((2*x^4*(-1 + x + 2*x^2 - 4*x^3 + 2*x^4))/(-2*x^2 + 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.
| \(\displaystyle \int \frac {\left (-48 x^{11}+80 x^{10}-32 x^9-24 x^8+16 x^7-4 x^6+4 x^5-2 x^3+\left (6 x^5-10 x^4+4 x^3\right ) \log ^3(x)+\left (-36 x^7+60 x^6-24 x^5-10 x^4+8 x^3\right ) \log ^2(x)+\left (72 x^9-120 x^8+48 x^7+32 x^6-24 x^5+2 x^4+2 x^3\right ) \log (x)\right ) \exp \left (\frac {4 x^{10}-8 x^9+4 x^8+4 x^7-4 x^6+x^4+\left (x^6-2 x^5+x^4\right ) \log ^2(x)+\left (-4 x^8+8 x^7-4 x^6-2 x^5+2 x^4\right ) \log (x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (48 x^{11}-80 x^{10}+32 x^9+24 x^8-16 x^7+4 x^6-4 x^5+2 x^3-\left (6 x^5-10 x^4+4 x^3\right ) \log ^3(x)-\left (-36 x^7+60 x^6-24 x^5-10 x^4+8 x^3\right ) \log ^2(x)-\left (72 x^9-120 x^8+48 x^7+32 x^6-24 x^5+2 x^4+2 x^3\right ) \log (x)\right ) \exp \left (\frac {x^4 \left (2 x^3-2 x^2-x \log (x)+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right )}{\left (2 x^2-\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2 \left (3 x^2-5 x+2\right ) x^3 \exp \left (\frac {x^4 \left (2 x^3-2 x^2-x \log (x)+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right )+\frac {2 (5 x-4) x^3 \exp \left (\frac {x^4 \left (2 x^3-2 x^2-x \log (x)+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right )}{2 x^2-\log (x)}-\frac {2 \left (4 x^3-4 x^2-x-1\right ) x^3 \exp \left (\frac {x^4 \left (2 x^3-2 x^2-x \log (x)+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right )}{\left (2 x^2-\log (x)\right )^2}-\frac {2 \left (4 x^2-1\right ) x^3 \exp \left (\frac {x^4 \left (2 x^3-2 x^2-x \log (x)+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right )}{\left (2 x^2-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \int \exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3dx-10 \int \exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4dx+2 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^3}dx+2 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^2}dx+2 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{\left (2 x^2-\log (x)\right )^2}dx-8 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{2 x^2-\log (x)}dx+10 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{2 x^2-\log (x)}dx-8 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^6}{\left (2 x^2-\log (x)\right )^2}dx+6 \int \exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5dx-8 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^3}dx+8 \int \frac {\exp \left (\frac {x^4 \left (2 x^3-2 x^2-\log (x) x+\log (x)+1\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^2}dx\) |
Int[(E^((x^4 - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + (2*x^4 - 2*x^5 - 4 *x^6 + 8*x^7 - 4*x^8)*Log[x] + (x^4 - 2*x^5 + x^6)*Log[x]^2)/(4*x^4 - 4*x^ 2*Log[x] + Log[x]^2))*(-2*x^3 + 4*x^5 - 4*x^6 + 16*x^7 - 24*x^8 - 32*x^9 + 80*x^10 - 48*x^11 + (2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120*x^8 + 72*x^9)*Log[x] + (8*x^3 - 10*x^4 - 24*x^5 + 60*x^6 - 36*x^7)*Log[x]^2 + ( 4*x^3 - 10*x^4 + 6*x^5)*Log[x]^3))/(-8*x^6 + 12*x^4*Log[x] - 6*x^2*Log[x]^ 2 + Log[x]^3),x]
3.18.5.3.1 Defintions of rubi rules used
Time = 24.36 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.09
| method | result | size |
| risch | \({\mathrm e}^{\frac {x^{4} \left (-2 x^{3}+x \ln \left (x \right )+2 x^{2}-\ln \left (x \right )-1\right )^{2}}{\left (-2 x^{2}+\ln \left (x \right )\right )^{2}}}\) | \(38\) |
| parallelrisch | \({\mathrm e}^{\frac {\left (x^{6}-2 x^{5}+x^{4}\right ) \ln \left (x \right )^{2}+\left (-4 x^{8}+8 x^{7}-4 x^{6}-2 x^{5}+2 x^{4}\right ) \ln \left (x \right )+4 x^{10}-8 x^{9}+4 x^{8}+4 x^{7}-4 x^{6}+x^{4}}{\ln \left (x \right )^{2}-4 x^{2} \ln \left (x \right )+4 x^{4}}}\) | \(97\) |
int(((6*x^5-10*x^4+4*x^3)*ln(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x^3)*ln( x)^2+(72*x^9-120*x^8+48*x^7+32*x^6-24*x^5+2*x^4+2*x^3)*ln(x)-48*x^11+80*x^ 10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)*ln(x)^2+(- 4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*ln(x)+4*x^10-8*x^9+4*x^8+4*x^7-4*x^6+x^4)/( ln(x)^2-4*x^2*ln(x)+4*x^4))/(ln(x)^3-6*x^2*ln(x)^2+12*x^4*ln(x)-8*x^6),x,m ethod=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (29) = 58\).
Time = 0.32 (sec) , antiderivative size = 95, normalized size of antiderivative = 2.71 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=e^{\left (\frac {4 \, x^{10} - 8 \, x^{9} + 4 \, x^{8} + 4 \, x^{7} - 4 \, x^{6} + x^{4} + {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} \log \left (x\right )^{2} - 2 \, {\left (2 \, x^{8} - 4 \, x^{7} + 2 \, x^{6} + x^{5} - x^{4}\right )} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}}\right )} \]
integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x ^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x ^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)*l og(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4 *x^6+x^4)/(log(x)^2-4*x^2*log(x)+4*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*l og(x)-8*x^6),x, algorithm=\
e^((4*x^10 - 8*x^9 + 4*x^8 + 4*x^7 - 4*x^6 + x^4 + (x^6 - 2*x^5 + x^4)*log (x)^2 - 2*(2*x^8 - 4*x^7 + 2*x^6 + x^5 - x^4)*log(x))/(4*x^4 - 4*x^2*log(x ) + log(x)^2))
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (22) = 44\).
Time = 0.58 (sec) , antiderivative size = 94, normalized size of antiderivative = 2.69 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=e^{\frac {4 x^{10} - 8 x^{9} + 4 x^{8} + 4 x^{7} - 4 x^{6} + x^{4} + \left (x^{6} - 2 x^{5} + x^{4}\right ) \log {\left (x \right )}^{2} + \left (- 4 x^{8} + 8 x^{7} - 4 x^{6} - 2 x^{5} + 2 x^{4}\right ) \log {\left (x \right )}}{4 x^{4} - 4 x^{2} \log {\left (x \right )} + \log {\left (x \right )}^{2}}} \]
integrate(((6*x**5-10*x**4+4*x**3)*ln(x)**3+(-36*x**7+60*x**6-24*x**5-10*x **4+8*x**3)*ln(x)**2+(72*x**9-120*x**8+48*x**7+32*x**6-24*x**5+2*x**4+2*x* *3)*ln(x)-48*x**11+80*x**10-32*x**9-24*x**8+16*x**7-4*x**6+4*x**5-2*x**3)* exp(((x**6-2*x**5+x**4)*ln(x)**2+(-4*x**8+8*x**7-4*x**6-2*x**5+2*x**4)*ln( x)+4*x**10-8*x**9+4*x**8+4*x**7-4*x**6+x**4)/(ln(x)**2-4*x**2*ln(x)+4*x**4 ))/(ln(x)**3-6*x**2*ln(x)**2+12*x**4*ln(x)-8*x**6),x)
exp((4*x**10 - 8*x**9 + 4*x**8 + 4*x**7 - 4*x**6 + x**4 + (x**6 - 2*x**5 + x**4)*log(x)**2 + (-4*x**8 + 8*x**7 - 4*x**6 - 2*x**5 + 2*x**4)*log(x))/( 4*x**4 - 4*x**2*log(x) + log(x)**2))
\[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=\int { \frac {2 \, {\left (24 \, x^{11} - 40 \, x^{10} + 16 \, x^{9} + 12 \, x^{8} - 8 \, x^{7} + 2 \, x^{6} - 2 \, x^{5} - {\left (3 \, x^{5} - 5 \, x^{4} + 2 \, x^{3}\right )} \log \left (x\right )^{3} + x^{3} + {\left (18 \, x^{7} - 30 \, x^{6} + 12 \, x^{5} + 5 \, x^{4} - 4 \, x^{3}\right )} \log \left (x\right )^{2} - {\left (36 \, x^{9} - 60 \, x^{8} + 24 \, x^{7} + 16 \, x^{6} - 12 \, x^{5} + x^{4} + x^{3}\right )} \log \left (x\right )\right )} e^{\left (\frac {4 \, x^{10} - 8 \, x^{9} + 4 \, x^{8} + 4 \, x^{7} - 4 \, x^{6} + x^{4} + {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} \log \left (x\right )^{2} - 2 \, {\left (2 \, x^{8} - 4 \, x^{7} + 2 \, x^{6} + x^{5} - x^{4}\right )} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}}\right )}}{8 \, x^{6} - 12 \, x^{4} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} - \log \left (x\right )^{3}} \,d x } \]
integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x ^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x ^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)*l og(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4 *x^6+x^4)/(log(x)^2-4*x^2*log(x)+4*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*l og(x)-8*x^6),x, algorithm=\
2*integrate((24*x^11 - 40*x^10 + 16*x^9 + 12*x^8 - 8*x^7 + 2*x^6 - 2*x^5 - (3*x^5 - 5*x^4 + 2*x^3)*log(x)^3 + x^3 + (18*x^7 - 30*x^6 + 12*x^5 + 5*x^ 4 - 4*x^3)*log(x)^2 - (36*x^9 - 60*x^8 + 24*x^7 + 16*x^6 - 12*x^5 + x^4 + x^3)*log(x))*e^((4*x^10 - 8*x^9 + 4*x^8 + 4*x^7 - 4*x^6 + x^4 + (x^6 - 2*x ^5 + x^4)*log(x)^2 - 2*(2*x^8 - 4*x^7 + 2*x^6 + x^5 - x^4)*log(x))/(4*x^4 - 4*x^2*log(x) + log(x)^2))/(8*x^6 - 12*x^4*log(x) + 6*x^2*log(x)^2 - log( x)^3), x)
Leaf count of result is larger than twice the leaf count of optimal. 357 vs. \(2 (29) = 58\).
Time = 0.78 (sec) , antiderivative size = 357, normalized size of antiderivative = 10.20 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=e^{\left (\frac {4 \, x^{10}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {8 \, x^{9}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {4 \, x^{8} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {4 \, x^{8}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {8 \, x^{7} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {x^{6} \log \left (x\right )^{2}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {4 \, x^{7}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {4 \, x^{6} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {2 \, x^{5} \log \left (x\right )^{2}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {4 \, x^{6}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} - \frac {2 \, x^{5} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {x^{4} \log \left (x\right )^{2}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {2 \, x^{4} \log \left (x\right )}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}} + \frac {x^{4}}{4 \, x^{4} - 4 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}}\right )} \]
integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x ^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x ^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)*l og(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4 *x^6+x^4)/(log(x)^2-4*x^2*log(x)+4*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*l og(x)-8*x^6),x, algorithm=\
e^(4*x^10/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 8*x^9/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 4*x^8*log(x)/(4*x^4 - 4*x^2*log(x) + log(x)^2) + 4*x^8/(4*x^ 4 - 4*x^2*log(x) + log(x)^2) + 8*x^7*log(x)/(4*x^4 - 4*x^2*log(x) + log(x) ^2) + x^6*log(x)^2/(4*x^4 - 4*x^2*log(x) + log(x)^2) + 4*x^7/(4*x^4 - 4*x^ 2*log(x) + log(x)^2) - 4*x^6*log(x)/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 2* x^5*log(x)^2/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 4*x^6/(4*x^4 - 4*x^2*log( x) + log(x)^2) - 2*x^5*log(x)/(4*x^4 - 4*x^2*log(x) + log(x)^2) + x^4*log( x)^2/(4*x^4 - 4*x^2*log(x) + log(x)^2) + 2*x^4*log(x)/(4*x^4 - 4*x^2*log(x ) + log(x)^2) + x^4/(4*x^4 - 4*x^2*log(x) + log(x)^2))
Time = 13.97 (sec) , antiderivative size = 284, normalized size of antiderivative = 8.11 \[ \int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx=\frac {{\mathrm {e}}^{\frac {x^4\,{\ln \left (x\right )}^2}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{\frac {x^6\,{\ln \left (x\right )}^2}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{-\frac {2\,x^5\,{\ln \left (x\right )}^2}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{\frac {x^4}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{-\frac {4\,x^6}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{\frac {4\,x^7}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{\frac {4\,x^8}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{\frac {4\,x^{10}}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}\,{\mathrm {e}}^{-\frac {8\,x^9}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}}{x^{\frac {2\,\left (2\,x^8-4\,x^7+2\,x^6+x^5-x^4\right )}{4\,x^4-4\,x^2\,\ln \left (x\right )+{\ln \left (x\right )}^2}}} \]
int(-(exp((x^4 - log(x)*(2*x^5 - 2*x^4 + 4*x^6 - 8*x^7 + 4*x^8) - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + log(x)^2*(x^4 - 2*x^5 + x^6))/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*(log(x)^2*(10*x^4 - 8*x^3 + 24*x^5 - 60*x^6 + 36*x ^7) - log(x)*(2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120*x^8 + 72*x^9) - log(x)^3*(4*x^3 - 10*x^4 + 6*x^5) + 2*x^3 - 4*x^5 + 4*x^6 - 16*x^7 + 24 *x^8 + 32*x^9 - 80*x^10 + 48*x^11))/(12*x^4*log(x) + log(x)^3 - 6*x^2*log( x)^2 - 8*x^6),x)
(exp((x^4*log(x)^2)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((x^6*log(x)^2)/ (log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp(-(2*x^5*log(x)^2)/(log(x)^2 - 4*x^2 *log(x) + 4*x^4))*exp(x^4/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp(-(4*x^6)/ (log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((4*x^7)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((4*x^8)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((4*x^10)/(log(x )^2 - 4*x^2*log(x) + 4*x^4))*exp(-(8*x^9)/(log(x)^2 - 4*x^2*log(x) + 4*x^4 )))/x^((2*(x^5 - x^4 + 2*x^6 - 4*x^7 + 2*x^8))/(log(x)^2 - 4*x^2*log(x) + 4*x^4))