\(\int \frac {(-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} (15 x^2+7 x^3-2 x^4)+e^x (40 x^3+2 x^4-2 x^5)+(-5+x) \log (4)) \log (x)+(-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+(4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)) \log (x)) \log (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4))+(-4+2 x+5 x^4+e^{2 x} (3 x^2+2 x^3)+e^x (8 x^3+2 x^4)-\log (4)) \log (x) \log (\log (x))}{(-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)) \log (x)} \, dx\) [157]

Optimal result

Integrand size = 263, antiderivative size = 30 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\log \left (x \left (-4+x+x^2 \left (e^x+x\right )^2-\log (4)\right )\right ) (5-x+\log (\log (x))) \]

[Out]

(ln(ln(x))+5-x)*ln(x*(x+(exp(x)+x)^2*x^2-4-2*ln(2)))

Rubi [F]

\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx \]

[In]

Int[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + E^x*(40*x^3 + 2*x^4 - 2*x^5) +
(-5 + x)*Log[4])*Log[x] + (-4 + x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 - 2*E^x*
x^4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5*x^4 +
E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8*x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3 + 2*E^
x*x^4 + x^5 - x*Log[4])*Log[x]),x]

[Out]

10*x + 12*Log[x] - x*Log[x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - 2*x*(2 + Log[2])] + 2*x*Log[Log[x]] + 3*Log[x]*
Log[Log[x]] - 2*LogIntegral[x] + 4*(2 + Log[2])*Defer[Int][(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/
2))^(-1), x] + (4*(2 + Log[2])*(27 + 4*Log[16])*Defer[Int][(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/
2))^(-1), x])/(8 + Log[16]) + 20*(2 + Log[2])*Defer[Int][1/(x*(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[
2]/2))), x] + (7 + Log[16])*Defer[Int][x/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 2*Defer[
Int][x^2/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 10*Defer[Int][(E^x*x^2)/(x + E^(2*x)*x^2
+ 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 10*Defer[Int][x^3/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log
[2]/2)), x] + 2*Defer[Int][(E^x*x^3)/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 2*Defer[Int]
[x^4/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 2*Defer[Int][(E^x*x^4)/(x + E^(2*x)*x^2 + 2*
E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 2*Defer[Int][x^5/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)
), x] + (17 + Log[16])*Defer[Int][x/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 2*Defer[Int]
[x^2/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 12*Defer[Int][(E^x*x^3)/(-x - E^(2*x)*x^2 -
2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 12*Defer[Int][x^4/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[
2]/2)), x] + 2*Defer[Int][(E^x*x^4)/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 2*Defer[Int]
[x^5/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + Defer[Int][Log[x^2 + E^(2*x)*x^3 + 2*E^x*x^
4 + x^5 - 4*x*(1 + Log[2]/2)]/(x*Log[x]), x] + (7 + Log[16])*Defer[Int][Log[Log[x]]/(x + E^(2*x)*x^2 + 2*E^x*x
^3 + x^4 - 4*(1 + Log[2]/2)), x] + 4*(2 + Log[2])*Defer[Int][Log[Log[x]]/(x*(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4
- 4*(1 + Log[2]/2))), x] + 2*Defer[Int][(E^x*x^2*Log[Log[x]])/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log
[2]/2)), x] + 2*Defer[Int][(x^3*Log[Log[x]])/(x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - 4*(1 + Log[2]/2)), x] + 2*De
fer[Int][(x*Log[Log[x]])/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 2*Defer[Int][(E^x*x^3*L
og[Log[x]])/(-x - E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x] + 2*Defer[Int][(x^4*Log[Log[x]])/(-x -
E^(2*x)*x^2 - 2*E^x*x^3 - x^4 + 4*(1 + Log[2]/2)), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (x^2+e^{2 x} x^3+2 e^x x^4+x^5+x (-4-\log (4))\right ) \log (x)} \, dx \\ & = \int \left (\frac {\left (2 x^2-2 e^x x^3-2 x^4+2 e^x x^4+2 x^5-8 \left (1+\frac {\log (2)}{2}\right )-7 x \left (1+\frac {4 \log (2)}{7}\right )\right ) (-5+x-\log (\log (x)))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )}+\frac {15 \log (x)+7 x \log (x)-2 x^2 \log (x)+\log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )-x \log (x) \log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )+3 \log (x) \log (\log (x))+2 x \log (x) \log (\log (x))}{x \log (x)}\right ) \, dx \\ & = \int \frac {\left (2 x^2-2 e^x x^3-2 x^4+2 e^x x^4+2 x^5-8 \left (1+\frac {\log (2)}{2}\right )-7 x \left (1+\frac {4 \log (2)}{7}\right )\right ) (-5+x-\log (\log (x)))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+\int \frac {15 \log (x)+7 x \log (x)-2 x^2 \log (x)+\log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )-x \log (x) \log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )+3 \log (x) \log (\log (x))+2 x \log (x) \log (\log (x))}{x \log (x)} \, dx \\ & = \int \left (\frac {15 \log (x)+7 x \log (x)-2 x^2 \log (x)+\log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )-x \log (x) \log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )}{x \log (x)}+\frac {(3+2 x) \log (\log (x))}{x}\right ) \, dx+\int \left (\frac {2 x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {10 e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {10 x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {12 e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {12 x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {20 (2+\log (2))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )}+\frac {10 x \left (1+\frac {1}{10} (7+\log (16))\right )}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {4 (-2-\log (2)) \left (1-\frac {5 (7+\log (16))}{8+\log (16)}\right )}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {4 (2+\log (2)) \log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )}+\frac {(7+\log (16)) \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}\right ) \, dx \\ & = 2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \frac {15 \log (x)+7 x \log (x)-2 x^2 \log (x)+\log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )-x \log (x) \log \left (x \left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)\right )\right )}{x \log (x)} \, dx+\int \frac {(3+2 x) \log (\log (x))}{x} \, dx \\ & = 2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \left (7+\frac {15}{x}-2 x+\left (-1+\frac {1}{x \log (x)}\right ) \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )\right ) \, dx+\int \left (2 \log (\log (x))+\frac {3 \log (\log (x))}{x}\right ) \, dx \\ & = 7 x-x^2+15 \log (x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \log (\log (x)) \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+3 \int \frac {\log (\log (x))}{x} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \left (-1+\frac {1}{x \log (x)}\right ) \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right ) \, dx \\ & = 7 x-x^2+12 \log (x)+2 x \log (\log (x))+3 \log (x) \log (\log (x))+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx-2 \int \frac {1}{\log (x)} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \left (-\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )+\frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)}\right ) \, dx \\ & = 7 x-x^2+12 \log (x)+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}-\int \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right ) \, dx+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ & = 7 x-x^2+12 \log (x)-x \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-2 x (2+\log (2))\right )+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \frac {2 x+3 e^{2 x} x^2+2 e^x \left (4+e^x\right ) x^3+\left (5+2 e^x\right ) x^4-2 (2+\log (2))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ & = 7 x-x^2+12 \log (x)-x \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-2 x (2+\log (2))\right )+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \left (3+2 x+\frac {-2 x^2+2 e^x x^3+2 x^4-2 e^x x^4-2 x^5+8 \left (1+\frac {\log (2)}{2}\right )+7 x \left (1+\frac {4 \log (2)}{7}\right )}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}\right ) \, dx+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ & = 10 x+12 \log (x)-x \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-2 x (2+\log (2))\right )+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \frac {-2 x^2+2 e^x x^3+2 x^4-2 e^x x^4-2 x^5+8 \left (1+\frac {\log (2)}{2}\right )+7 x \left (1+\frac {4 \log (2)}{7}\right )}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ & = 10 x+12 \log (x)-x \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-2 x (2+\log (2))\right )+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \left (\frac {2 e^x x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^2}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 e^x x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {2 x^5}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )}+\frac {4 (2+\log (2))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}+\frac {x (7+\log (16))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )}\right ) \, dx+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ & = 10 x+12 \log (x)-x \log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-2 x (2+\log (2))\right )+2 x \log (\log (x))+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+2 \int \frac {x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^2}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^5}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^2 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^3 \log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+2 \int \frac {x^4 \log (\log (x))}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {e^x x^2}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+10 \int \frac {x^3}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {e^x x^3}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+12 \int \frac {x^4}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(4 (2+\log (2))) \int \frac {\log (\log (x))}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(20 (2+\log (2))) \int \frac {1}{x \left (x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )\right )} \, dx+(7+\log (16)) \int \frac {x}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(7+\log (16)) \int \frac {\log (\log (x))}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx+(17+\log (16)) \int \frac {x}{-x-e^{2 x} x^2-2 e^x x^3-x^4+4 \left (1+\frac {\log (2)}{2}\right )} \, dx+\frac {(4 (2+\log (2)) (27+4 \log (16))) \int \frac {1}{x+e^{2 x} x^2+2 e^x x^3+x^4-4 \left (1+\frac {\log (2)}{2}\right )} \, dx}{8+\log (16)}+\int \frac {\log \left (x^2+e^{2 x} x^3+2 e^x x^4+x^5-4 x \left (1+\frac {\log (2)}{2}\right )\right )}{x \log (x)} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx \]

[In]

Integrate[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + E^x*(40*x^3 + 2*x^4 - 2*x
^5) + (-5 + x)*Log[4])*Log[x] + (-4 + x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 -
2*E^x*x^4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5
*x^4 + E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8*x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3
+ 2*E^x*x^4 + x^5 - x*Log[4])*Log[x]),x]

[Out]

Integrate[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + E^x*(40*x^3 + 2*x^4 - 2*x
^5) + (-5 + x)*Log[4])*Log[x] + (-4 + x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 -
2*E^x*x^4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5
*x^4 + E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8*x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3
+ 2*E^x*x^4 + x^5 - x*Log[4])*Log[x]), x]

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.06 (sec) , antiderivative size = 666, normalized size of antiderivative = 22.20

\[\text {Expression too large to display}\]

[In]

int((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*ln(2)+5*x^4+2*x-4)*ln(x)*ln(ln(x))+((-exp(x)^2*x^3-2*exp(x
)*x^4+2*x*ln(2)-x^5-x^2+4*x)*ln(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*ln(2)+x^4+x-4)*ln(exp(x)^2*x^3+2*exp(x)*x^4-2*x
*ln(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+40*x^3)*exp(x)+2*(-5+x)*ln(2)-5*x^5+25*x^4-2
*x^2+14*x-20)*ln(x))/(exp(x)^2*x^3+2*exp(x)*x^4-2*x*ln(2)+x^5+x^2-4*x)/ln(x),x)

[Out]

(ln(ln(x))-x)*ln(-1/2*x^4-exp(x)*x^3-1/2*exp(2*x)*x^2+ln(2)-1/2*x+2)+ln(x)*ln(ln(x))-x*ln(x)+1/2*I*Pi*ln(ln(x)
)*csgn(I*x)*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2+I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+
1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2+1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^
3-1/2*I*Pi*x*csgn(I*x)*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2-1/2*I*Pi*ln(ln(x))*csgn
(I*x)*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-
ln(2)+1/2*x-2)*x)+I*Pi*ln(ln(x))+1/2*I*Pi*x*csgn(I*x)*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-
2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)-I*Pi*ln(ln(x))*csgn(I*(1/2*x^4+exp(x)*x^3+1/
2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2+1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn
(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2+15*ln(x)+5*ln(exp(2*x)+2*exp(x)*x-(-x^4+2*ln(2)-x+
4)/x^2)-1/2*I*Pi*ln(ln(x))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^3-1/2*I*Pi*ln(ln(x))*
csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+
1/2*x-2)*x)^2-I*Pi*x

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (30) = 60\).

Time = 0.26 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.40 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=-{\left (x - 5\right )} \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) + \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) \log \left (\log \left (x\right )\right ) \]

[In]

integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x-4)*log(x)*log(log(x))+((-exp(x)^2*x
^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x)*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*
exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+40*x^3)*exp(x)+2*(-5+x)*log(2
)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(exp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="
fricas")

[Out]

-(x - 5)*log(x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x) + log(x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2
- 2*x*log(2) - 4*x)*log(log(x))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (29) = 58\).

Time = 38.94 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.53 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\left (- x + \log {\left (\log {\left (x \right )} \right )}\right ) \log {\left (x^{5} + 2 x^{4} e^{x} + x^{3} e^{2 x} + x^{2} - 4 x - 2 x \log {\left (2 \right )} \right )} + 15 \log {\left (x \right )} + 5 \log {\left (2 x e^{x} + e^{2 x} + \frac {x^{4} + x - 4 - 2 \log {\left (2 \right )}}{x^{2}} \right )} \]

[In]

integrate((((2*x**3+3*x**2)*exp(x)**2+(2*x**4+8*x**3)*exp(x)-2*ln(2)+5*x**4+2*x-4)*ln(x)*ln(ln(x))+((-exp(x)**
2*x**3-2*exp(x)*x**4+2*x*ln(2)-x**5-x**2+4*x)*ln(x)+exp(x)**2*x**2+2*exp(x)*x**3-2*ln(2)+x**4+x-4)*ln(exp(x)**
2*x**3+2*exp(x)*x**4-2*x*ln(2)+x**5+x**2-4*x)+((-2*x**4+7*x**3+15*x**2)*exp(x)**2+(-2*x**5+2*x**4+40*x**3)*exp
(x)+2*(-5+x)*ln(2)-5*x**5+25*x**4-2*x**2+14*x-20)*ln(x))/(exp(x)**2*x**3+2*exp(x)*x**4-2*x*ln(2)+x**5+x**2-4*x
)/ln(x),x)

[Out]

(-x + log(log(x)))*log(x**5 + 2*x**4*exp(x) + x**3*exp(2*x) + x**2 - 4*x - 2*x*log(2)) + 15*log(x) + 5*log(2*x
*exp(x) + exp(2*x) + (x**4 + x - 4 - 2*log(2))/x**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (30) = 60\).

Time = 0.38 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.70 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=-{\left (x - \log \left (\log \left (x\right )\right )\right )} \log \left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x - 2 \, \log \left (2\right ) - 4\right ) - {\left (x - 15\right )} \log \left (x\right ) + \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 5 \, \log \left (\frac {x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x - 2 \, \log \left (2\right ) - 4}{x^{2}}\right ) \]

[In]

integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x-4)*log(x)*log(log(x))+((-exp(x)^2*x
^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x)*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*
exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+40*x^3)*exp(x)+2*(-5+x)*log(2
)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(exp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="
maxima")

[Out]

-(x - log(log(x)))*log(x^4 + 2*x^3*e^x + x^2*e^(2*x) + x - 2*log(2) - 4) - (x - 15)*log(x) + log(x)*log(log(x)
) + 5*log((x^4 + 2*x^3*e^x + x^2*e^(2*x) + x - 2*log(2) - 4)/x^2)

Giac [F]

\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int { \frac {{\left (5 \, x^{4} + {\left (2 \, x^{3} + 3 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{4} + 4 \, x^{3}\right )} e^{x} + 2 \, x - 2 \, \log \left (2\right ) - 4\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + {\left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} - {\left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right )} \log \left (x\right ) + x - 2 \, \log \left (2\right ) - 4\right )} \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) - {\left (5 \, x^{5} - 25 \, x^{4} + 2 \, x^{2} + {\left (2 \, x^{4} - 7 \, x^{3} - 15 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - x^{4} - 20 \, x^{3}\right )} e^{x} - 2 \, {\left (x - 5\right )} \log \left (2\right ) - 14 \, x + 20\right )} \log \left (x\right )}{{\left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right )} \log \left (x\right )} \,d x } \]

[In]

integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x-4)*log(x)*log(log(x))+((-exp(x)^2*x
^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x)*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*
exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+40*x^3)*exp(x)+2*(-5+x)*log(2
)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(exp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="
giac")

[Out]

integrate(((5*x^4 + (2*x^3 + 3*x^2)*e^(2*x) + 2*(x^4 + 4*x^3)*e^x + 2*x - 2*log(2) - 4)*log(x)*log(log(x)) + (
x^4 + 2*x^3*e^x + x^2*e^(2*x) - (x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x)*log(x) + x - 2*log(2)
- 4)*log(x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x) - (5*x^5 - 25*x^4 + 2*x^2 + (2*x^4 - 7*x^3 -
15*x^2)*e^(2*x) + 2*(x^5 - x^4 - 20*x^3)*e^x - 2*(x - 5)*log(2) - 14*x + 20)*log(x))/((x^5 + 2*x^4*e^x + x^3*
e^(2*x) + x^2 - 2*x*log(2) - 4*x)*log(x)), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\ln \left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )\,\left (x-2\,\ln \left (2\right )+2\,x^3\,{\mathrm {e}}^x+x^2\,{\mathrm {e}}^{2\,x}+x^4-\ln \left (x\right )\,\left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )-4\right )+\ln \left (x\right )\,\left (14\,x+{\mathrm {e}}^x\,\left (-2\,x^5+2\,x^4+40\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (-2\,x^4+7\,x^3+15\,x^2\right )+2\,\ln \left (2\right )\,\left (x-5\right )-2\,x^2+25\,x^4-5\,x^5-20\right )+\ln \left (\ln \left (x\right )\right )\,\ln \left (x\right )\,\left (2\,x-2\,\ln \left (2\right )+{\mathrm {e}}^x\,\left (2\,x^4+8\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (2\,x^3+3\,x^2\right )+5\,x^4-4\right )}{\ln \left (x\right )\,\left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )} \,d x \]

[In]

int((log(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)*(x - 2*log(2) + 2*x^3*exp(x) + x^2*exp(2*
x) + x^4 - log(x)*(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5) - 4) + log(x)*(14*x + exp(x)*(4
0*x^3 + 2*x^4 - 2*x^5) + exp(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + 2*log(2)*(x - 5) - 2*x^2 + 25*x^4 - 5*x^5 - 20) +
log(log(x))*log(x)*(2*x - 2*log(2) + exp(x)*(8*x^3 + 2*x^4) + exp(2*x)*(3*x^2 + 2*x^3) + 5*x^4 - 4))/(log(x)*
(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)),x)

[Out]

int((log(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)*(x - 2*log(2) + 2*x^3*exp(x) + x^2*exp(2*
x) + x^4 - log(x)*(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5) - 4) + log(x)*(14*x + exp(x)*(4
0*x^3 + 2*x^4 - 2*x^5) + exp(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + 2*log(2)*(x - 5) - 2*x^2 + 25*x^4 - 5*x^5 - 20) +
log(log(x))*log(x)*(2*x - 2*log(2) + exp(x)*(8*x^3 + 2*x^4) + exp(2*x)*(3*x^2 + 2*x^3) + 5*x^4 - 4))/(log(x)*
(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)), x)