Integrand size = 278, antiderivative size = 34 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4 (1+x)))\right )}{x}} x \]
Time = 0.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=e x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \]
Integrate[(6*x^2 + E^3*x^2 - x^3 + (-7*x^2 - 6*x^3 + x^4 + E^3*(-x^2 - x^3 ) + (7*x + 6*x^2 - x^3 + E^3*(x + x^2))*Log[4 + 4*x])*Log[x - Log[4 + 4*x] ] + (-6*x - 5*x^2 + x^3 + E^3*(-x - x^2) + (6 + 5*x - x^2 + E^3*(1 + x))*L og[4 + 4*x])*Log[x - Log[4 + 4*x]]*Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]] ])/(E^((-x + Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]]])/x)*(-6*x^2 - 5*x^3 + x^4 + E^3*(-x^2 - x^3) + (6*x + 5*x^2 - x^3 + E^3*(x + x^2))*Log[4 + 4*x ])*Log[x - Log[4 + 4*x]]),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.
| \(\displaystyle \int \frac {\left (-x^3+e^3 x^2+6 x^2+\left (x^3-5 x^2+e^3 \left (-x^2-x\right )+\left (-x^2+5 x+e^3 (x+1)+6\right ) \log (4 x+4)-6 x\right ) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )+\left (x^4-6 x^3-7 x^2+e^3 \left (-x^3-x^2\right )+\left (-x^3+6 x^2+e^3 \left (x^2+x\right )+7 x\right ) \log (4 x+4)\right ) \log (x-\log (4 x+4))\right ) \exp \left (-\frac {\log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )-x}{x}\right )}{\left (x^4-5 x^3-6 x^2+e^3 \left (-x^3-x^2\right )+\left (-x^3+5 x^2+e^3 \left (x^2+x\right )+6 x\right ) \log (4 x+4)\right ) \log (x-\log (4 x+4))} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (-x^3+\left (6+e^3\right ) x^2+\left (x^3-5 x^2+e^3 \left (-x^2-x\right )+\left (-x^2+5 x+e^3 (x+1)+6\right ) \log (4 x+4)-6 x\right ) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )+\left (x^4-6 x^3-7 x^2+e^3 \left (-x^3-x^2\right )+\left (-x^3+6 x^2+e^3 \left (x^2+x\right )+7 x\right ) \log (4 x+4)\right ) \log (x-\log (4 x+4))\right ) \exp \left (-\frac {\log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )-x}{x}\right )}{\left (x^4-5 x^3-6 x^2+e^3 \left (-x^3-x^2\right )+\left (-x^3+5 x^2+e^3 \left (x^2+x\right )+6 x\right ) \log (4 x+4)\right ) \log (x-\log (4 x+4))}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-\frac {1}{x}-1} \left (x^3-\left (6+e^3\right ) x^2-(x+1) \left (x-e^3-7\right ) x (x-\log (4 x+4)) \log (x-\log (4 x+4))-(x+1) \left (x-e^3-6\right ) (x-\log (4 x+4)) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )\right )}{x (x+1) (x-\log (4 x+4))}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle e \int -\frac {\left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}} \left (-x^3+\left (6+e^3\right ) x^2-\left (-x+e^3+7\right ) (x+1) (x-\log (4 x+4)) \log (x-\log (4 x+4)) x-\left (-x+e^3+6\right ) (x+1) (x-\log (4 x+4)) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )\right )}{x (x+1) (x-\log (4 x+4))}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -e \int \frac {\left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}} \left (-x^3+\left (6+e^3\right ) x^2-\left (-x+e^3+7\right ) (x+1) (x-\log (4 x+4)) \log (x-\log (4 x+4)) x-\left (-x+e^3+6\right ) (x+1) (x-\log (4 x+4)) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )\right )}{x (x+1) (x-\log (4 x+4))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -e \int \left (\frac {\left (\log (x-\log (4 x+4)) x^3-\log (4 x+4) \log (x-\log (4 x+4)) x^2-6 \left (1+\frac {e^3}{6}\right ) \log (x-\log (4 x+4)) x^2-x^2+6 \left (1+\frac {e^3}{6}\right ) \log (4 x+4) \log (x-\log (4 x+4)) x-7 \left (1+\frac {e^3}{7}\right ) \log (x-\log (4 x+4)) x+6 \left (1+\frac {e^3}{6}\right ) x+7 \left (1+\frac {e^3}{7}\right ) \log (4 x+4) \log (x-\log (4 x+4))\right ) \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}}{(x+1) (x-\log (4 x+4))}+\frac {\left (x-e^3-6\right ) \log (x-\log (4 x+4)) \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right ) \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}}{x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -e \left (\left (7+e^3\right ) \int \frac {\left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}}{x-\log (4 x+4)}dx-\int \frac {x \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}}{x-\log (4 x+4)}dx-\left (7+e^3\right ) \int \frac {\left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}}{(x+1) (x-\log (4 x+4))}dx-\left (7+e^3\right ) \int \log (x-\log (4 x+4)) \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}dx+\int x \log (x-\log (4 x+4)) \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1-\frac {1}{x}}dx-\int \frac {\left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )^{-1/x} \log \left (\left (-x+e^3+6\right ) \log (x-\log (4 x+4))\right )}{x}dx\right )\) |
Int[(6*x^2 + E^3*x^2 - x^3 + (-7*x^2 - 6*x^3 + x^4 + E^3*(-x^2 - x^3) + (7 *x + 6*x^2 - x^3 + E^3*(x + x^2))*Log[4 + 4*x])*Log[x - Log[4 + 4*x]] + (- 6*x - 5*x^2 + x^3 + E^3*(-x - x^2) + (6 + 5*x - x^2 + E^3*(1 + x))*Log[4 + 4*x])*Log[x - Log[4 + 4*x]]*Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]]])/(E^ ((-x + Log[(6 + E^3 - x)*Log[x - Log[4 + 4*x]]])/x)*(-6*x^2 - 5*x^3 + x^4 + E^3*(-x^2 - x^3) + (6*x + 5*x^2 - x^3 + E^3*(x + x^2))*Log[4 + 4*x])*Log [x - Log[4 + 4*x]]),x]
3.11.2.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.27 (sec) , antiderivative size = 205, normalized size of antiderivative = 6.03
\[x \left ({\mathrm e}^{3}-x +6\right )^{-\frac {1}{x}} \ln \left (-\ln \left (4+4 x \right )+x \right )^{-\frac {1}{x}} {\mathrm e}^{\frac {i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{3}-i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{2} \operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right )\right )-i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{2} \operatorname {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )+i \pi \,\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right ) \operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right )\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )+2 x}{2 x}}\]
int(((((1+x)*exp(3)-x^2+5*x+6)*ln(4+4*x)+(-x^2-x)*exp(3)+x^3-5*x^2-6*x)*ln (-ln(4+4*x)+x)*ln((exp(3)-x+6)*ln(-ln(4+4*x)+x))+(((x^2+x)*exp(3)-x^3+6*x^ 2+7*x)*ln(4+4*x)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*ln(-ln(4+4*x)+x)+x^2*e xp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*ln(4+4*x)+(-x^3-x^2)*exp( 3)+x^4-5*x^3-6*x^2)/ln(-ln(4+4*x)+x)/exp((ln((exp(3)-x+6)*ln(-ln(4+4*x)+x) )-x)/x),x)
x/((exp(3)-x+6)^(1/x))/(ln(-ln(4+4*x)+x)^(1/x))*exp(1/2*(I*Pi*csgn(I*ln(-l n(4+4*x)+x)*(exp(3)-x+6))^3-I*Pi*csgn(I*ln(-ln(4+4*x)+x)*(exp(3)-x+6))^2*c sgn(I*ln(-ln(4+4*x)+x))-I*Pi*csgn(I*ln(-ln(4+4*x)+x)*(exp(3)-x+6))^2*csgn( I*(exp(3)-x+6))+I*Pi*csgn(I*ln(-ln(4+4*x)+x)*(exp(3)-x+6))*csgn(I*ln(-ln(4 +4*x)+x))*csgn(I*(exp(3)-x+6))+2*x)/x)
Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=x e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )} \]
integrate(((((1+x)*exp(3)-x^2+5*x+6)*log(4+4*x)+(-x^2-x)*exp(3)+x^3-5*x^2- 6*x)*log(-log(4+4*x)+x)*log((exp(3)-x+6)*log(-log(4+4*x)+x))+(((x^2+x)*exp (3)-x^3+6*x^2+7*x)*log(4+4*x)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-log( 4+4*x)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4+4*x) +(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2)/log(-log(4+4*x)+x)/exp((log((exp(3)-x+ 6)*log(-log(4+4*x)+x))-x)/x),x, algorithm=\
Timed out. \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\text {Timed out} \]
integrate(((((1+x)*exp(3)-x**2+5*x+6)*ln(4+4*x)+(-x**2-x)*exp(3)+x**3-5*x* *2-6*x)*ln(-ln(4+4*x)+x)*ln((exp(3)-x+6)*ln(-ln(4+4*x)+x))+(((x**2+x)*exp( 3)-x**3+6*x**2+7*x)*ln(4+4*x)+(-x**3-x**2)*exp(3)+x**4-6*x**3-7*x**2)*ln(- ln(4+4*x)+x)+x**2*exp(3)-x**3+6*x**2)/(((x**2+x)*exp(3)-x**3+5*x**2+6*x)*l n(4+4*x)+(-x**3-x**2)*exp(3)+x**4-5*x**3-6*x**2)/ln(-ln(4+4*x)+x)/exp((ln( (exp(3)-x+6)*ln(-ln(4+4*x)+x))-x)/x),x)
Time = 0.46 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.09 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=x e^{\left (-\frac {\log \left (-x + e^{3} + 6\right )}{x} - \frac {\log \left (\log \left (x - 2 \, \log \left (2\right ) - \log \left (x + 1\right )\right )\right )}{x} + 1\right )} \]
integrate(((((1+x)*exp(3)-x^2+5*x+6)*log(4+4*x)+(-x^2-x)*exp(3)+x^3-5*x^2- 6*x)*log(-log(4+4*x)+x)*log((exp(3)-x+6)*log(-log(4+4*x)+x))+(((x^2+x)*exp (3)-x^3+6*x^2+7*x)*log(4+4*x)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-log( 4+4*x)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4+4*x) +(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2)/log(-log(4+4*x)+x)/exp((log((exp(3)-x+ 6)*log(-log(4+4*x)+x))-x)/x),x, algorithm=\
\[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\int { -\frac {{\left (x^{3} - x^{2} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - {\left (x^{2} - {\left (x + 1\right )} e^{3} - 5 \, x - 6\right )} \log \left (4 \, x + 4\right ) - 6 \, x\right )} \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right ) \log \left (x - \log \left (4 \, x + 4\right )\right ) - 6 \, x^{2} - {\left (x^{4} - 6 \, x^{3} - 7 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 6 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 7 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )} e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )}}{{\left (x^{4} - 5 \, x^{3} - 6 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 6 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )} \,d x } \]
integrate(((((1+x)*exp(3)-x^2+5*x+6)*log(4+4*x)+(-x^2-x)*exp(3)+x^3-5*x^2- 6*x)*log(-log(4+4*x)+x)*log((exp(3)-x+6)*log(-log(4+4*x)+x))+(((x^2+x)*exp (3)-x^3+6*x^2+7*x)*log(4+4*x)+(-x^3-x^2)*exp(3)+x^4-6*x^3-7*x^2)*log(-log( 4+4*x)+x)+x^2*exp(3)-x^3+6*x^2)/(((x^2+x)*exp(3)-x^3+5*x^2+6*x)*log(4+4*x) +(-x^3-x^2)*exp(3)+x^4-5*x^3-6*x^2)/log(-log(4+4*x)+x)/exp((log((exp(3)-x+ 6)*log(-log(4+4*x)+x))-x)/x),x, algorithm=\
integrate(-(x^3 - x^2*e^3 - (x^3 - 5*x^2 - (x^2 + x)*e^3 - (x^2 - (x + 1)* e^3 - 5*x - 6)*log(4*x + 4) - 6*x)*log(-(x - e^3 - 6)*log(x - log(4*x + 4) ))*log(x - log(4*x + 4)) - 6*x^2 - (x^4 - 6*x^3 - 7*x^2 - (x^3 + x^2)*e^3 - (x^3 - 6*x^2 - (x^2 + x)*e^3 - 7*x)*log(4*x + 4))*log(x - log(4*x + 4))) *e^((x - log(-(x - e^3 - 6)*log(x - log(4*x + 4))))/x)/((x^4 - 5*x^3 - 6*x ^2 - (x^3 + x^2)*e^3 - (x^3 - 5*x^2 - (x^2 + x)*e^3 - 6*x)*log(4*x + 4))*l og(x - log(4*x + 4))), x)
Time = 19.38 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.53 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\frac {x\,\mathrm {e}}{{\left (6\,\ln \left (x-\ln \left (4\,x+4\right )\right )+\ln \left (x-\ln \left (4\,x+4\right )\right )\,{\mathrm {e}}^3-x\,\ln \left (x-\ln \left (4\,x+4\right )\right )\right )}^{1/x}} \]
int((exp((x - log(log(x - log(4*x + 4))*(exp(3) - x + 6)))/x)*(log(x - log (4*x + 4))*(exp(3)*(x^2 + x^3) - log(4*x + 4)*(7*x + exp(3)*(x + x^2) + 6* x^2 - x^3) + 7*x^2 + 6*x^3 - x^4) - x^2*exp(3) - 6*x^2 + x^3 + log(x - log (4*x + 4))*log(log(x - log(4*x + 4))*(exp(3) - x + 6))*(6*x - log(4*x + 4) *(5*x + exp(3)*(x + 1) - x^2 + 6) + exp(3)*(x + x^2) + 5*x^2 - x^3)))/(log (x - log(4*x + 4))*(exp(3)*(x^2 + x^3) - log(4*x + 4)*(6*x + exp(3)*(x + x ^2) + 5*x^2 - x^3) + 6*x^2 + 5*x^3 - x^4)),x)