Integrand size = 209, antiderivative size = 27 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4}{x^2 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \]
Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4}{x^2 \log ^2\left (5-x+16 \log ^2\left (\frac {1}{x}\right ) (-10+\log (x))^2\right )} \]
Integrate[(8*x + 25600*Log[x^(-1)] + 2560*Log[x^(-1)]^2 + (-5120*Log[x^(-1 )] - 256*Log[x^(-1)]^2)*Log[x] + 256*Log[x^(-1)]*Log[x]^2 + (-40 + 8*x - 1 2800*Log[x^(-1)]^2 + 2560*Log[x^(-1)]^2*Log[x] - 128*Log[x^(-1)]^2*Log[x]^ 2)*Log[5 - x + 1600*Log[x^(-1)]^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(- 1)]^2*Log[x]^2])/((5*x^3 - x^4 + 1600*x^3*Log[x^(-1)]^2 - 320*x^3*Log[x^(- 1)]^2*Log[x] + 16*x^3*Log[x^(-1)]^2*Log[x]^2)*Log[5 - x + 1600*Log[x^(-1)] ^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2]^3),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.
| \(\displaystyle \int \frac {8 x+2560 \log ^2\left (\frac {1}{x}\right )+256 \log ^2(x) \log \left (\frac {1}{x}\right )+\left (-256 \log ^2\left (\frac {1}{x}\right )-5120 \log \left (\frac {1}{x}\right )\right ) \log (x)+\left (8 x-128 \log ^2(x) \log ^2\left (\frac {1}{x}\right )+2560 \log (x) \log ^2\left (\frac {1}{x}\right )-12800 \log ^2\left (\frac {1}{x}\right )-40\right ) \log \left (-x+16 \log ^2(x) \log ^2\left (\frac {1}{x}\right )-320 \log (x) \log ^2\left (\frac {1}{x}\right )+1600 \log ^2\left (\frac {1}{x}\right )+5\right )+25600 \log \left (\frac {1}{x}\right )}{\left (-x^4+5 x^3+1600 x^3 \log ^2\left (\frac {1}{x}\right )+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)\right ) \log ^3\left (-x+16 \log ^2(x) \log ^2\left (\frac {1}{x}\right )-320 \log (x) \log ^2\left (\frac {1}{x}\right )+1600 \log ^2\left (\frac {1}{x}\right )+5\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (x-16 (\log (x)-10) \left ((\log (x)-10) \log \left (-x+16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+5\right )+2\right ) \log ^2\left (\frac {1}{x}\right )+(x-5) \log \left (-x+16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+5\right )+32 (\log (x)-10)^2 \log \left (\frac {1}{x}\right )\right )}{x^3 \left (-x+16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+5\right ) \log ^3\left (-x+16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+5\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 8 \int \frac {16 (10-\log (x)) \left (2-(10-\log (x)) \log \left (16 \log ^2\left (\frac {1}{x}\right ) (10-\log (x))^2-x+5\right )\right ) \log ^2\left (\frac {1}{x}\right )+32 (10-\log (x))^2 \log \left (\frac {1}{x}\right )+x-(5-x) \log \left (16 \log ^2\left (\frac {1}{x}\right ) (10-\log (x))^2-x+5\right )}{x^3 \left (16 \log ^2\left (\frac {1}{x}\right ) (10-\log (x))^2-x+5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (10-\log (x))^2-x+5\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {32 \log (x) \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right )-32 \log ^2(x) \log \left (\frac {1}{x}\right )+640 \log (x) \log \left (\frac {1}{x}\right )-3200 \log \left (\frac {1}{x}\right )-x}{x^3 \left (-16 \log ^2(x) \log ^2\left (\frac {1}{x}\right )+320 \log (x) \log ^2\left (\frac {1}{x}\right )-1600 \log ^2\left (\frac {1}{x}\right )+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}-\frac {1}{x^3 \log ^2\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 8 \left (-\int \frac {1}{x^3 \log ^2\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx-3200 \int \frac {\log \left (\frac {1}{x}\right )}{x^3 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx-320 \int \frac {\log ^2\left (\frac {1}{x}\right )}{x^3 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx+640 \int \frac {\log \left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx+32 \int \frac {\log ^2\left (\frac {1}{x}\right ) \log (x)}{x^3 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx-32 \int \frac {\log \left (\frac {1}{x}\right ) \log ^2(x)}{x^3 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx-\int \frac {1}{x^2 \left (-16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2+x-5\right ) \log ^3\left (16 \log ^2\left (\frac {1}{x}\right ) (\log (x)-10)^2-x+5\right )}dx\right )\) |
Int[(8*x + 25600*Log[x^(-1)] + 2560*Log[x^(-1)]^2 + (-5120*Log[x^(-1)] - 2 56*Log[x^(-1)]^2)*Log[x] + 256*Log[x^(-1)]*Log[x]^2 + (-40 + 8*x - 12800*L og[x^(-1)]^2 + 2560*Log[x^(-1)]^2*Log[x] - 128*Log[x^(-1)]^2*Log[x]^2)*Log [5 - x + 1600*Log[x^(-1)]^2 - 320*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2* Log[x]^2])/((5*x^3 - x^4 + 1600*x^3*Log[x^(-1)]^2 - 320*x^3*Log[x^(-1)]^2* Log[x] + 16*x^3*Log[x^(-1)]^2*Log[x]^2)*Log[5 - x + 1600*Log[x^(-1)]^2 - 3 20*Log[x^(-1)]^2*Log[x] + 16*Log[x^(-1)]^2*Log[x]^2]^3),x]
3.4.85.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 155.72 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19
| method | result | size |
| risch | \(\frac {4}{x^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )^{2}}\) | \(32\) |
| parallelrisch | \(\frac {4}{x^{2} \ln \left (16 \ln \left (\frac {1}{x}\right )^{2} \ln \left (x \right )^{2}-320 \ln \left (\frac {1}{x}\right )^{2} \ln \left (x \right )+1600 \ln \left (\frac {1}{x}\right )^{2}+5-x \right )^{2}}\) | \(44\) |
| derivativedivides | \(\frac {128 \ln \left (x \right )^{4}-2560 \ln \left (x \right )^{3}+12800 \ln \left (x \right )^{2}+40-8 x}{\left (64 \ln \left (x \right )^{3}-960 \ln \left (x \right )^{2}+3200 \ln \left (x \right )-x \right ) x^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )}-\frac {4 \left (32 \ln \left (x \right )^{4} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )-640 \ln \left (x \right )^{3} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )-64 \ln \left (x \right )^{3}+3200 \ln \left (x \right )^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )+960 \ln \left (x \right )^{2}-2 x \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )+x -3200 \ln \left (x \right )+10 \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )\right )}{x^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )^{2} \left (64 \ln \left (x \right )^{3}-960 \ln \left (x \right )^{2}+3200 \ln \left (x \right )-x \right )}\) | \(292\) |
| default | \(\frac {128 \ln \left (x \right )^{4}-2560 \ln \left (x \right )^{3}+12800 \ln \left (x \right )^{2}+40-8 x}{\left (64 \ln \left (x \right )^{3}-960 \ln \left (x \right )^{2}+3200 \ln \left (x \right )-x \right ) x^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )}-\frac {4 \left (32 \ln \left (x \right )^{4} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )-640 \ln \left (x \right )^{3} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )-64 \ln \left (x \right )^{3}+3200 \ln \left (x \right )^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )+960 \ln \left (x \right )^{2}-2 x \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )+x -3200 \ln \left (x \right )+10 \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )\right )}{x^{2} \ln \left (16 \ln \left (x \right )^{4}-320 \ln \left (x \right )^{3}+1600 \ln \left (x \right )^{2}+5-x \right )^{2} \left (64 \ln \left (x \right )^{3}-960 \ln \left (x \right )^{2}+3200 \ln \left (x \right )-x \right )}\) | \(292\) |
int(((-128*ln(1/x)^2*ln(x)^2+2560*ln(1/x)^2*ln(x)-12800*ln(1/x)^2+8*x-40)* ln(16*ln(1/x)^2*ln(x)^2-320*ln(1/x)^2*ln(x)+1600*ln(1/x)^2+5-x)+256*ln(1/x )*ln(x)^2+(-256*ln(1/x)^2-5120*ln(1/x))*ln(x)+2560*ln(1/x)^2+25600*ln(1/x) +8*x)/(16*x^3*ln(1/x)^2*ln(x)^2-320*x^3*ln(1/x)^2*ln(x)+1600*x^3*ln(1/x)^2 -x^4+5*x^3)/ln(16*ln(1/x)^2*ln(x)^2-320*ln(1/x)^2*ln(x)+1600*ln(1/x)^2+5-x )^3,x,method=_RETURNVERBOSE)
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4}{x^{2} \log \left (16 \, \log \left (\frac {1}{x}\right )^{4} + 320 \, \log \left (\frac {1}{x}\right )^{3} + 1600 \, \log \left (\frac {1}{x}\right )^{2} - x + 5\right )^{2}} \]
integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x) ^2+8*x-40)*log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^ 2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560*l og(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x) ^2*log(x)+1600*x^3*log(1/x)^2-x^4+5*x^3)/log(16*log(1/x)^2*log(x)^2-320*lo g(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm=\
Time = 0.18 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4}{x^{2} \log {\left (- x + 16 \log {\left (x \right )}^{4} - 320 \log {\left (x \right )}^{3} + 1600 \log {\left (x \right )}^{2} + 5 \right )}^{2}} \]
integrate(((-128*ln(1/x)**2*ln(x)**2+2560*ln(1/x)**2*ln(x)-12800*ln(1/x)** 2+8*x-40)*ln(16*ln(1/x)**2*ln(x)**2-320*ln(1/x)**2*ln(x)+1600*ln(1/x)**2+5 -x)+256*ln(1/x)*ln(x)**2+(-256*ln(1/x)**2-5120*ln(1/x))*ln(x)+2560*ln(1/x) **2+25600*ln(1/x)+8*x)/(16*x**3*ln(1/x)**2*ln(x)**2-320*x**3*ln(1/x)**2*ln (x)+1600*x**3*ln(1/x)**2-x**4+5*x**3)/ln(16*ln(1/x)**2*ln(x)**2-320*ln(1/x )**2*ln(x)+1600*ln(1/x)**2+5-x)**3,x)
Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4}{x^{2} \log \left (16 \, \log \left (x\right )^{4} - 320 \, \log \left (x\right )^{3} + 1600 \, \log \left (x\right )^{2} - x + 5\right )^{2}} \]
integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x) ^2+8*x-40)*log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^ 2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560*l og(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x) ^2*log(x)+1600*x^3*log(1/x)^2-x^4+5*x^3)/log(16*log(1/x)^2*log(x)^2-320*lo g(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 159 vs. \(2 (27) = 54\).
Time = 0.43 (sec) , antiderivative size = 159, normalized size of antiderivative = 5.89 \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\frac {4 \, {\left (64 \, \log \left (x\right )^{3} - 960 \, \log \left (x\right )^{2} - x + 3200 \, \log \left (x\right )\right )}}{64 \, x^{2} \log \left (16 \, \log \left (x\right )^{4} - 320 \, \log \left (x\right )^{3} + 1600 \, \log \left (x\right )^{2} - x + 5\right )^{2} \log \left (x\right )^{3} - 960 \, x^{2} \log \left (16 \, \log \left (x\right )^{4} - 320 \, \log \left (x\right )^{3} + 1600 \, \log \left (x\right )^{2} - x + 5\right )^{2} \log \left (x\right )^{2} - x^{3} \log \left (16 \, \log \left (x\right )^{4} - 320 \, \log \left (x\right )^{3} + 1600 \, \log \left (x\right )^{2} - x + 5\right )^{2} + 3200 \, x^{2} \log \left (16 \, \log \left (x\right )^{4} - 320 \, \log \left (x\right )^{3} + 1600 \, \log \left (x\right )^{2} - x + 5\right )^{2} \log \left (x\right )} \]
integrate(((-128*log(1/x)^2*log(x)^2+2560*log(1/x)^2*log(x)-12800*log(1/x) ^2+8*x-40)*log(16*log(1/x)^2*log(x)^2-320*log(1/x)^2*log(x)+1600*log(1/x)^ 2+5-x)+256*log(1/x)*log(x)^2+(-256*log(1/x)^2-5120*log(1/x))*log(x)+2560*l og(1/x)^2+25600*log(1/x)+8*x)/(16*x^3*log(1/x)^2*log(x)^2-320*x^3*log(1/x) ^2*log(x)+1600*x^3*log(1/x)^2-x^4+5*x^3)/log(16*log(1/x)^2*log(x)^2-320*lo g(1/x)^2*log(x)+1600*log(1/x)^2+5-x)^3,x, algorithm=\
4*(64*log(x)^3 - 960*log(x)^2 - x + 3200*log(x))/(64*x^2*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2*log(x)^3 - 960*x^2*log(16*log(x)^ 4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2*log(x)^2 - x^3*log(16*log(x)^4 - 320*log(x)^3 + 1600*log(x)^2 - x + 5)^2 + 3200*x^2*log(16*log(x)^4 - 32 0*log(x)^3 + 1600*log(x)^2 - x + 5)^2*log(x))
Timed out. \[ \int \frac {8 x+25600 \log \left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right )+\left (-5120 \log \left (\frac {1}{x}\right )-256 \log ^2\left (\frac {1}{x}\right )\right ) \log (x)+256 \log \left (\frac {1}{x}\right ) \log ^2(x)+\left (-40+8 x-12800 \log ^2\left (\frac {1}{x}\right )+2560 \log ^2\left (\frac {1}{x}\right ) \log (x)-128 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log \left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )}{\left (5 x^3-x^4+1600 x^3 \log ^2\left (\frac {1}{x}\right )-320 x^3 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 x^3 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right ) \log ^3\left (5-x+1600 \log ^2\left (\frac {1}{x}\right )-320 \log ^2\left (\frac {1}{x}\right ) \log (x)+16 \log ^2\left (\frac {1}{x}\right ) \log ^2(x)\right )} \, dx=\int \frac {8\,x+25600\,\ln \left (\frac {1}{x}\right )-\ln \left (x\right )\,\left (256\,{\ln \left (\frac {1}{x}\right )}^2+5120\,\ln \left (\frac {1}{x}\right )\right )-\ln \left (16\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \left (x\right )}^2-320\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \left (x\right )+1600\,{\ln \left (\frac {1}{x}\right )}^2-x+5\right )\,\left (128\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \left (x\right )}^2-2560\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \left (x\right )+12800\,{\ln \left (\frac {1}{x}\right )}^2-8\,x+40\right )+2560\,{\ln \left (\frac {1}{x}\right )}^2+256\,\ln \left (\frac {1}{x}\right )\,{\ln \left (x\right )}^2}{{\ln \left (16\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \left (x\right )}^2-320\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \left (x\right )+1600\,{\ln \left (\frac {1}{x}\right )}^2-x+5\right )}^3\,\left (-x^4+16\,x^3\,{\ln \left (\frac {1}{x}\right )}^2\,{\ln \left (x\right )}^2-320\,x^3\,{\ln \left (\frac {1}{x}\right )}^2\,\ln \left (x\right )+1600\,x^3\,{\ln \left (\frac {1}{x}\right )}^2+5\,x^3\right )} \,d x \]
int((8*x + 25600*log(1/x) - log(x)*(5120*log(1/x) + 256*log(1/x)^2) - log( 16*log(1/x)^2*log(x)^2 - x + 1600*log(1/x)^2 - 320*log(1/x)^2*log(x) + 5)* (128*log(1/x)^2*log(x)^2 - 8*x + 12800*log(1/x)^2 - 2560*log(1/x)^2*log(x) + 40) + 2560*log(1/x)^2 + 256*log(1/x)*log(x)^2)/(log(16*log(1/x)^2*log(x )^2 - x + 1600*log(1/x)^2 - 320*log(1/x)^2*log(x) + 5)^3*(5*x^3 - x^4 + 16 00*x^3*log(1/x)^2 + 16*x^3*log(1/x)^2*log(x)^2 - 320*x^3*log(1/x)^2*log(x) )),x)
int((8*x + 25600*log(1/x) - log(x)*(5120*log(1/x) + 256*log(1/x)^2) - log( 16*log(1/x)^2*log(x)^2 - x + 1600*log(1/x)^2 - 320*log(1/x)^2*log(x) + 5)* (128*log(1/x)^2*log(x)^2 - 8*x + 12800*log(1/x)^2 - 2560*log(1/x)^2*log(x) + 40) + 2560*log(1/x)^2 + 256*log(1/x)*log(x)^2)/(log(16*log(1/x)^2*log(x )^2 - x + 1600*log(1/x)^2 - 320*log(1/x)^2*log(x) + 5)^3*(5*x^3 - x^4 + 16 00*x^3*log(1/x)^2 + 16*x^3*log(1/x)^2*log(x)^2 - 320*x^3*log(1/x)^2*log(x) )), x)