Integrand size = 243, antiderivative size = 36 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {e^{1-x} x (x-\log (2+x))}{\log \left (\log \left (\frac {x^2}{\left (-x+(4+x)^2\right )^2}\right )\right )} \]
Time = 0.27 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.97 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {e^{1-x} x (x-\log (2+x))}{\log \left (\log \left (\frac {x^2}{\left (16+7 x+x^2\right )^2}\right )\right )} \]
Integrate[(E^(1 - x)*(-64*x - 32*x^2 + 4*x^3 + 2*x^4 + (64 + 32*x - 4*x^2 - 2*x^3)*Log[2 + x] + ((48*x + 21*x^2 - 13*x^3 - 7*x^4 - x^5)*Log[x^2/(256 + 224*x + 81*x^2 + 14*x^3 + x^4)] + (-32 + 2*x + 21*x^2 + 8*x^3 + x^4)*Lo g[2 + x]*Log[x^2/(256 + 224*x + 81*x^2 + 14*x^3 + x^4)])*Log[Log[x^2/(256 + 224*x + 81*x^2 + 14*x^3 + x^4)]]))/((32 + 30*x + 9*x^2 + x^3)*Log[x^2/(2 56 + 224*x + 81*x^2 + 14*x^3 + x^4)]*Log[Log[x^2/(256 + 224*x + 81*x^2 + 1 4*x^3 + x^4)]]^2),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.
| \(\displaystyle \int \frac {e^{1-x} \left (2 x^4+4 x^3-32 x^2+\left (-2 x^3-4 x^2+32 x+64\right ) \log (x+2)+\left (\left (x^4+8 x^3+21 x^2+2 x-32\right ) \log (x+2) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )+\left (-x^5-7 x^4-13 x^3+21 x^2+48 x\right ) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right ) \log \left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )-64 x\right )}{\left (x^3+9 x^2+30 x+32\right ) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right ) \log ^2\left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {e^{1-x} \left (2 x^4+4 x^3-32 x^2+\left (-2 x^3-4 x^2+32 x+64\right ) \log (x+2)+\left (\left (x^4+8 x^3+21 x^2+2 x-32\right ) \log (x+2) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )+\left (-x^5-7 x^4-13 x^3+21 x^2+48 x\right ) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right ) \log \left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )-64 x\right )}{6 (x+2) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right ) \log ^2\left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )}+\frac {e^{1-x} (-x-5) \left (2 x^4+4 x^3-32 x^2+\left (-2 x^3-4 x^2+32 x+64\right ) \log (x+2)+\left (\left (x^4+8 x^3+21 x^2+2 x-32\right ) \log (x+2) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )+\left (-x^5-7 x^4-13 x^3+21 x^2+48 x\right ) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right ) \log \left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )-64 x\right )}{6 \left (x^2+7 x+16\right ) \log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right ) \log ^2\left (\log \left (\frac {x^2}{x^4+14 x^3+81 x^2+224 x+256}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{1-x} \left ((x+2) \log (x+2) \left (-2 x^2+\left (x^3+6 x^2+9 x-16\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log \left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )+32\right )-x \left (-2 x^3-4 x^2+\left (x^4+7 x^3+13 x^2-21 x-48\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log \left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )+32 x+64\right )\right )}{(x+2) \left (x^2+7 x+16\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log ^2\left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle \int \left (\frac {2 e^{1-x} \left (x^2-16\right ) (x-\log (x+2))}{\left (x^2+7 x+16\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log ^2\left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}+\frac {e^{1-x} \left (-x^3+x^2 \log (x+2)+3 x+x \log (x+2)-2 \log (x+2)\right )}{(x+2) \log \left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{1-x} \left (x^2-16\right ) (x-\log (x+2))}{\left (x^2+7 x+16\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log ^2\left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}-\frac {e^{1-x} \left (x^3-x^2 \log (x+2)-3 x-x \log (x+2)+2 \log (x+2)\right )}{(x+2) \log \left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {2 e^{1-x} \left (x^2-16\right ) (x-\log (x+2))}{\left (x^2+7 x+16\right ) \log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right ) \log ^2\left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}-\frac {e^{1-x} \left (x^3-x^2 \log (x+2)-3 x-x \log (x+2)+2 \log (x+2)\right )}{(x+2) \log \left (\log \left (\frac {x^2}{\left (x^2+7 x+16\right )^2}\right )\right )}\right )dx\) |
Int[(E^(1 - x)*(-64*x - 32*x^2 + 4*x^3 + 2*x^4 + (64 + 32*x - 4*x^2 - 2*x^ 3)*Log[2 + x] + ((48*x + 21*x^2 - 13*x^3 - 7*x^4 - x^5)*Log[x^2/(256 + 224 *x + 81*x^2 + 14*x^3 + x^4)] + (-32 + 2*x + 21*x^2 + 8*x^3 + x^4)*Log[2 + x]*Log[x^2/(256 + 224*x + 81*x^2 + 14*x^3 + x^4)])*Log[Log[x^2/(256 + 224* x + 81*x^2 + 14*x^3 + x^4)]]))/((32 + 30*x + 9*x^2 + x^3)*Log[x^2/(256 + 2 24*x + 81*x^2 + 14*x^3 + x^4)]*Log[Log[x^2/(256 + 224*x + 81*x^2 + 14*x^3 + x^4)]]^2),x]
3.9.40.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Int[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[ {v = RationalFunctionExpand[u/(a + b*x^n + c*x^(2*n)), x]}, Int[v, x] /; Su mQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.11 (sec) , antiderivative size = 195, normalized size of antiderivative = 5.42
\[\frac {x \left (x -\ln \left (2+x \right )\right ) {\mathrm e}^{1-x}}{\ln \left (2 \ln \left (x \right )-2 \ln \left (x^{2}+7 x +16\right )+\frac {i \pi \,\operatorname {csgn}\left (i \left (x^{2}+7 x +16\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \left (x^{2}+7 x +16\right )^{2}\right )+\operatorname {csgn}\left (i \left (x^{2}+7 x +16\right )\right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x^{2}}{\left (x^{2}+7 x +16\right )^{2}}\right ) \left (-\operatorname {csgn}\left (\frac {i x^{2}}{\left (x^{2}+7 x +16\right )^{2}}\right )+\operatorname {csgn}\left (i x^{2}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x^{2}}{\left (x^{2}+7 x +16\right )^{2}}\right )+\operatorname {csgn}\left (\frac {i}{\left (x^{2}+7 x +16\right )^{2}}\right )\right )}{2}\right )}\]
int((((x^4+8*x^3+21*x^2+2*x-32)*ln(x^2/(x^4+14*x^3+81*x^2+224*x+256))*ln(2 +x)+(-x^5-7*x^4-13*x^3+21*x^2+48*x)*ln(x^2/(x^4+14*x^3+81*x^2+224*x+256))) *ln(ln(x^2/(x^4+14*x^3+81*x^2+224*x+256)))+(-2*x^3-4*x^2+32*x+64)*ln(2+x)+ 2*x^4+4*x^3-32*x^2-64*x)/(x^3+9*x^2+30*x+32)/exp(-1+x)/ln(x^2/(x^4+14*x^3+ 81*x^2+224*x+256))/ln(ln(x^2/(x^4+14*x^3+81*x^2+224*x+256)))^2,x)
x*(x-ln(2+x))*exp(1-x)/ln(2*ln(x)-2*ln(x^2+7*x+16)+1/2*I*Pi*csgn(I*(x^2+7* x+16)^2)*(-csgn(I*(x^2+7*x+16)^2)+csgn(I*(x^2+7*x+16)))^2-1/2*I*Pi*csgn(I* x^2)*(-csgn(I*x^2)+csgn(I*x))^2-1/2*I*Pi*csgn(I*x^2/(x^2+7*x+16)^2)*(-csgn (I*x^2/(x^2+7*x+16)^2)+csgn(I*x^2))*(-csgn(I*x^2/(x^2+7*x+16)^2)+csgn(I/(x ^2+7*x+16)^2)))
Time = 0.26 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.47 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {x^{2} e^{\left (-x + 1\right )} - x e^{\left (-x + 1\right )} \log \left (x + 2\right )}{\log \left (\log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right )\right )} \]
integrate((((x^4+8*x^3+21*x^2+2*x-32)*log(x^2/(x^4+14*x^3+81*x^2+224*x+256 ))*log(2+x)+(-x^5-7*x^4-13*x^3+21*x^2+48*x)*log(x^2/(x^4+14*x^3+81*x^2+224 *x+256)))*log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)))+(-2*x^3-4*x^2+32*x+6 4)*log(2+x)+2*x^4+4*x^3-32*x^2-64*x)/(x^3+9*x^2+30*x+32)/exp(-1+x)/log(x^2 /(x^4+14*x^3+81*x^2+224*x+256))/log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)) )^2,x, algorithm=\
(x^2*e^(-x + 1) - x*e^(-x + 1)*log(x + 2))/log(log(x^2/(x^4 + 14*x^3 + 81* x^2 + 224*x + 256)))
Time = 1.52 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.08 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {\left (x^{2} - x \log {\left (x + 2 \right )}\right ) e^{1 - x}}{\log {\left (\log {\left (\frac {x^{2}}{x^{4} + 14 x^{3} + 81 x^{2} + 224 x + 256} \right )} \right )}} \]
integrate((((x**4+8*x**3+21*x**2+2*x-32)*ln(x**2/(x**4+14*x**3+81*x**2+224 *x+256))*ln(2+x)+(-x**5-7*x**4-13*x**3+21*x**2+48*x)*ln(x**2/(x**4+14*x**3 +81*x**2+224*x+256)))*ln(ln(x**2/(x**4+14*x**3+81*x**2+224*x+256)))+(-2*x* *3-4*x**2+32*x+64)*ln(2+x)+2*x**4+4*x**3-32*x**2-64*x)/(x**3+9*x**2+30*x+3 2)/exp(-1+x)/ln(x**2/(x**4+14*x**3+81*x**2+224*x+256))/ln(ln(x**2/(x**4+14 *x**3+81*x**2+224*x+256)))**2,x)
Result contains complex when optimal does not.
Time = 0.39 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.31 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {x^{2} e - x e \log \left (x + 2\right )}{{\left (i \, \pi + \log \left (2\right )\right )} e^{x} + e^{x} \log \left (\log \left (x^{2} + 7 \, x + 16\right ) - \log \left (x\right )\right )} \]
integrate((((x^4+8*x^3+21*x^2+2*x-32)*log(x^2/(x^4+14*x^3+81*x^2+224*x+256 ))*log(2+x)+(-x^5-7*x^4-13*x^3+21*x^2+48*x)*log(x^2/(x^4+14*x^3+81*x^2+224 *x+256)))*log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)))+(-2*x^3-4*x^2+32*x+6 4)*log(2+x)+2*x^4+4*x^3-32*x^2-64*x)/(x^3+9*x^2+30*x+32)/exp(-1+x)/log(x^2 /(x^4+14*x^3+81*x^2+224*x+256))/log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)) )^2,x, algorithm=\
\[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\int { \frac {{\left (2 \, x^{4} + 4 \, x^{3} - 32 \, x^{2} - 2 \, {\left (x^{3} + 2 \, x^{2} - 16 \, x - 32\right )} \log \left (x + 2\right ) + {\left ({\left (x^{4} + 8 \, x^{3} + 21 \, x^{2} + 2 \, x - 32\right )} \log \left (x + 2\right ) \log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right ) - {\left (x^{5} + 7 \, x^{4} + 13 \, x^{3} - 21 \, x^{2} - 48 \, x\right )} \log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right )\right )} \log \left (\log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right )\right ) - 64 \, x\right )} e^{\left (-x + 1\right )}}{{\left (x^{3} + 9 \, x^{2} + 30 \, x + 32\right )} \log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right ) \log \left (\log \left (\frac {x^{2}}{x^{4} + 14 \, x^{3} + 81 \, x^{2} + 224 \, x + 256}\right )\right )^{2}} \,d x } \]
integrate((((x^4+8*x^3+21*x^2+2*x-32)*log(x^2/(x^4+14*x^3+81*x^2+224*x+256 ))*log(2+x)+(-x^5-7*x^4-13*x^3+21*x^2+48*x)*log(x^2/(x^4+14*x^3+81*x^2+224 *x+256)))*log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)))+(-2*x^3-4*x^2+32*x+6 4)*log(2+x)+2*x^4+4*x^3-32*x^2-64*x)/(x^3+9*x^2+30*x+32)/exp(-1+x)/log(x^2 /(x^4+14*x^3+81*x^2+224*x+256))/log(log(x^2/(x^4+14*x^3+81*x^2+224*x+256)) )^2,x, algorithm=\
Time = 10.47 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.28 \[ \int \frac {e^{1-x} \left (-64 x-32 x^2+4 x^3+2 x^4+\left (64+32 x-4 x^2-2 x^3\right ) \log (2+x)+\left (\left (48 x+21 x^2-13 x^3-7 x^4-x^5\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )+\left (-32+2 x+21 x^2+8 x^3+x^4\right ) \log (2+x) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right ) \log \left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )\right )}{\left (32+30 x+9 x^2+x^3\right ) \log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right ) \log ^2\left (\log \left (\frac {x^2}{256+224 x+81 x^2+14 x^3+x^4}\right )\right )} \, dx=\frac {x^2\,{\mathrm {e}}^{1-x}}{\ln \left (\ln \left (x^2\right )-\ln \left (x^4+14\,x^3+81\,x^2+224\,x+256\right )\right )}-\frac {x\,\ln \left (x+2\right )\,{\mathrm {e}}^{1-x}}{\ln \left (\ln \left (x^2\right )-\ln \left (x^4+14\,x^3+81\,x^2+224\,x+256\right )\right )} \]
int(-(exp(1 - x)*(64*x - log(x + 2)*(32*x - 4*x^2 - 2*x^3 + 64) + 32*x^2 - 4*x^3 - 2*x^4 + log(log(x^2/(224*x + 81*x^2 + 14*x^3 + x^4 + 256)))*(log( x^2/(224*x + 81*x^2 + 14*x^3 + x^4 + 256))*(13*x^3 - 21*x^2 - 48*x + 7*x^4 + x^5) - log(x + 2)*log(x^2/(224*x + 81*x^2 + 14*x^3 + x^4 + 256))*(2*x + 21*x^2 + 8*x^3 + x^4 - 32))))/(log(x^2/(224*x + 81*x^2 + 14*x^3 + x^4 + 2 56))*log(log(x^2/(224*x + 81*x^2 + 14*x^3 + x^4 + 256)))^2*(30*x + 9*x^2 + x^3 + 32)),x)