Integrand size = 161, antiderivative size = 24 \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\frac {x}{\log \left (x \log (x) \left (4-\log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )\right )} \]
Time = 0.11 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\frac {x}{\log \left (-x \log (x) \left (-4+\left (2+\log \left (\log \left (\frac {1}{x}\right )\right )\right )^2\right )\right )} \]
Integrate[(4*Log[x^(-1)] + 4*Log[x^(-1)]*Log[x] + 2*Log[x]*Log[E^2*Log[x^( -1)]] + (-Log[x^(-1)] - Log[x^(-1)]*Log[x])*Log[E^2*Log[x^(-1)]]^2 + (-4*L og[x^(-1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*Log [x] - x*Log[x]*Log[E^2*Log[x^(-1)]]^2])/((-4*Log[x^(-1)]*Log[x] + Log[x^(- 1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*Log[x] - x*Log[x]*Log[E^2*Log[x ^(-1)]]^2]^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.
| \(\displaystyle \int \frac {\left (-\log (x) \log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right )\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )-4 \log \left (\frac {1}{x}\right ) \log (x)\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)}{\left (\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )-4 \log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-\log (x) \log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right )\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )-4 \log \left (\frac {1}{x}\right ) \log (x)\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)}{\log \left (\frac {1}{x}\right ) \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {-\log \left (\frac {1}{x}\right ) \log ^2\left (\log \left (\frac {1}{x}\right )\right )-\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (\log \left (\frac {1}{x}\right )\right )-4 \log \left (\frac {1}{x}\right ) \log \left (\log \left (\frac {1}{x}\right )\right )-4 \log \left (\frac {1}{x}\right ) \log (x) \log \left (\log \left (\frac {1}{x}\right )\right )+2 \log (x) \log \left (\log \left (\frac {1}{x}\right )\right )+4 \log (x)}{\log \left (\frac {1}{x}\right ) \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}+\frac {1}{\log \left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \int \frac {1}{\left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx+2 \int \frac {1}{\log \left (\frac {1}{x}\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx-4 \int \frac {1}{\log (x) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx+4 \int \frac {1}{\log \left (\frac {1}{x}\right ) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx-\int \frac {\log \left (\log \left (\frac {1}{x}\right )\right )}{\left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx-\int \frac {\log \left (\log \left (\frac {1}{x}\right )\right )}{\log (x) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right ) \log ^2\left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx+\int \frac {1}{\log \left (-x \log (x) \log \left (\log \left (\frac {1}{x}\right )\right ) \left (\log \left (\log \left (\frac {1}{x}\right )\right )+4\right )\right )}dx\) |
Int[(4*Log[x^(-1)] + 4*Log[x^(-1)]*Log[x] + 2*Log[x]*Log[E^2*Log[x^(-1)]] + (-Log[x^(-1)] - Log[x^(-1)]*Log[x])*Log[E^2*Log[x^(-1)]]^2 + (-4*Log[x^( -1)]*Log[x] + Log[x^(-1)]*Log[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*Log[x] - x*Log[x]*Log[E^2*Log[x^(-1)]]^2])/((-4*Log[x^(-1)]*Log[x] + Log[x^(-1)]*Lo g[x]*Log[E^2*Log[x^(-1)]]^2)*Log[4*x*Log[x] - x*Log[x]*Log[E^2*Log[x^(-1)] ]^2]^2),x]
3.3.18.3.1 Defintions of rubi rules used
\[\int \frac {\left (\ln \left (\frac {1}{x}\right ) \ln \left (x \right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}-4 \ln \left (\frac {1}{x}\right ) \ln \left (x \right )\right ) \ln \left (-x \ln \left (x \right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+4 x \ln \left (x \right )\right )+\left (-\ln \left (\frac {1}{x}\right ) \ln \left (x \right )-\ln \left (\frac {1}{x}\right )\right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+2 \ln \left (x \right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )+4 \ln \left (\frac {1}{x}\right ) \ln \left (x \right )+4 \ln \left (\frac {1}{x}\right )}{\left (\ln \left (\frac {1}{x}\right ) \ln \left (x \right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}-4 \ln \left (\frac {1}{x}\right ) \ln \left (x \right )\right ) {\ln \left (-x \ln \left (x \right ) \ln \left ({\mathrm e}^{2} \ln \left (\frac {1}{x}\right )\right )^{2}+4 x \ln \left (x \right )\right )}^{2}}d x\]
int(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))*ln(-x*ln(x)*ln(e xp(2)*ln(1/x))^2+4*x*ln(x))+(-ln(1/x)*ln(x)-ln(1/x))*ln(exp(2)*ln(1/x))^2+ 2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*ln(x)*ln(ex p(2)*ln(1/x))^2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x ))^2,x)
int(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))^2-4*ln(1/x)*ln(x))*ln(-x*ln(x)*ln(e xp(2)*ln(1/x))^2+4*x*ln(x))+(-ln(1/x)*ln(x)-ln(1/x))*ln(exp(2)*ln(1/x))^2+ 2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*ln(x)*ln(ex p(2)*ln(1/x))^2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))^2+4*x*ln(x ))^2,x)
Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\frac {x}{\log \left (x \log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (\frac {1}{x}\right ) - 4 \, x \log \left (\frac {1}{x}\right )\right )} \]
integrate(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log( -x*log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))+(-log(1/x)*log(x)-log(1/x))*l og(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*lo g(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x* log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))^2,x, algorithm=\
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\frac {x}{\log {\left (- x \log {\left (x \right )} \log {\left (- e^{2} \log {\left (x \right )} \right )}^{2} + 4 x \log {\left (x \right )} \right )}} \]
integrate(((ln(1/x)*ln(x)*ln(exp(2)*ln(1/x))**2-4*ln(1/x)*ln(x))*ln(-x*ln( x)*ln(exp(2)*ln(1/x))**2+4*x*ln(x))+(-ln(1/x)*ln(x)-ln(1/x))*ln(exp(2)*ln( 1/x))**2+2*ln(x)*ln(exp(2)*ln(1/x))+4*ln(1/x)*ln(x)+4*ln(1/x))/(ln(1/x)*ln (x)*ln(exp(2)*ln(1/x))**2-4*ln(1/x)*ln(x))/ln(-x*ln(x)*ln(exp(2)*ln(1/x))* *2+4*x*ln(x))**2,x)
\[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\int { -\frac {{\left (\log \left (x\right ) \log \left (\frac {1}{x}\right ) + \log \left (\frac {1}{x}\right )\right )} \log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} - {\left (\log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (x\right ) \log \left (\frac {1}{x}\right ) - 4 \, \log \left (x\right ) \log \left (\frac {1}{x}\right )\right )} \log \left (-x \log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (x\right ) + 4 \, x \log \left (x\right )\right ) - 2 \, \log \left (e^{2} \log \left (\frac {1}{x}\right )\right ) \log \left (x\right ) - 4 \, \log \left (x\right ) \log \left (\frac {1}{x}\right ) - 4 \, \log \left (\frac {1}{x}\right )}{{\left (\log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (x\right ) \log \left (\frac {1}{x}\right ) - 4 \, \log \left (x\right ) \log \left (\frac {1}{x}\right )\right )} \log \left (-x \log \left (e^{2} \log \left (\frac {1}{x}\right )\right )^{2} \log \left (x\right ) + 4 \, x \log \left (x\right )\right )^{2}} \,d x } \]
integrate(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log( -x*log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))+(-log(1/x)*log(x)-log(1/x))*l og(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*lo g(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x* log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))^2,x, algorithm=\
(((4*I*pi - pi^2)*x*log(x) + (x*log(x) + x)*log(log(x))^2 + (6*I*pi - pi^2 + 4)*x - 2*((-I*pi - 2)*x*log(x) + (-I*pi - 3)*x)*log(log(x)))*log(-log(x ))^2 - 4*((-4*I*pi + pi^2)*x*log(x) - (x*log(x) + x)*log(log(x))^2 + (-6*I *pi + pi^2 - 4)*x + 2*((-I*pi - 2)*x*log(x) + (-I*pi - 3)*x)*log(log(x)))* log(-log(x)))/(((log(x) + 1)*log(log(x))^3 + (4*I*pi - pi^2)*log(x)^2 + (2 *I*pi + (2*I*pi + 5)*log(x) + log(x)^2 + 4)*log(log(x))^2 + (4*I*pi - pi^2 )*log(x) + (4*I*pi - 2*(-I*pi - 2)*log(x)^2 - pi^2 + (6*I*pi - pi^2 + 4)*l og(x))*log(log(x)))*log(-log(x))^2 - 4*(-2*I*pi - log(x) - 4)*log(log(x))^ 2 + 4*log(log(x))^3 - 4*(-4*I*pi + pi^2)*log(x) + 2*((2*log(x) + 3)*log(lo g(x))^3 - 2*(-4*I*pi + pi^2)*log(x)^2 - (-6*I*pi + (-4*I*pi - 11)*log(x) - 2*log(x)^2 - 12)*log(log(x))^2 - 3*(-4*I*pi + pi^2)*log(x) - (-12*I*pi + 4*(-I*pi - 2)*log(x)^2 + 3*pi^2 + 2*(-7*I*pi + pi^2 - 6)*log(x))*log(log(x )))*log(-log(x)) + (16*I*pi + (4*I*pi + (log(x) + 1)*log(log(x))^2 - pi^2 + (4*I*pi - pi^2)*log(x) - 2*(-I*pi + (-I*pi - 2)*log(x) - 2)*log(log(x))) *log(-log(x))^2 - 4*pi^2 - 2*(-12*I*pi - (2*log(x) + 3)*log(log(x))^2 + 3* pi^2 + 2*(-4*I*pi + pi^2)*log(x) + 2*(-3*I*pi + 2*(-I*pi - 2)*log(x) - 6)* log(log(x)))*log(-log(x)) - 8*(-I*pi - 2)*log(log(x)) + 4*log(log(x))^2)*l og(-log(-log(x)) - 4) - 4*(-4*I*pi + pi^2 + 2*(-I*pi - 2)*log(x))*log(log( x)) + (16*I*pi + (4*I*pi + (log(x) + 1)*log(log(x))^2 - pi^2 + (4*I*pi - p i^2)*log(x) - 2*(-I*pi + (-I*pi - 2)*log(x) - 2)*log(log(x)))*log(-log(...
Result contains complex when optimal does not.
Time = 0.65 (sec) , antiderivative size = 1664, normalized size of antiderivative = 69.33 \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=\text {Too large to display} \]
integrate(((log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))*log( -x*log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))+(-log(1/x)*log(x)-log(1/x))*l og(exp(2)*log(1/x))^2+2*log(x)*log(exp(2)*log(1/x))+4*log(1/x)*log(x)+4*lo g(1/x))/(log(1/x)*log(x)*log(exp(2)*log(1/x))^2-4*log(1/x)*log(x))/log(-x* log(x)*log(exp(2)*log(1/x))^2+4*x*log(x))^2,x, algorithm=\
(pi^2*x*log(x)*log(-log(x))^2 - 2*I*pi*x*log(x)*log(-log(x))^2*log(log(x)) - x*log(x)*log(-log(x))^2*log(log(x))^2 + 4*pi^2*x*log(x)*log(-log(x)) + pi^2*x*log(-log(x))^2 - 4*I*pi*x*log(x)*log(-log(x))^2 - 8*I*pi*x*log(x)*l og(-log(x))*log(log(x)) - 2*I*pi*x*log(-log(x))^2*log(log(x)) - 4*x*log(x) *log(-log(x))^2*log(log(x)) - 4*x*log(x)*log(-log(x))*log(log(x))^2 - x*lo g(-log(x))^2*log(log(x))^2 + 4*pi^2*x*log(-log(x)) - 16*I*pi*x*log(x)*log( -log(x)) - 6*I*pi*x*log(-log(x))^2 - 8*I*pi*x*log(-log(x))*log(log(x)) - 1 6*x*log(x)*log(-log(x))*log(log(x)) - 6*x*log(-log(x))^2*log(log(x)) - 4*x *log(-log(x))*log(log(x))^2 - 24*I*pi*x*log(-log(x)) - 4*x*log(-log(x))^2 - 24*x*log(-log(x))*log(log(x)) - 16*x*log(-log(x)))/(I*pi^3*log(x)*log(-l og(x))^2 + pi^2*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^ 2 + pi^2*log(x)^2*log(-log(x))^2 + 3*pi^2*log(x)*log(-log(x))^2*log(log(x) ) - 2*I*pi*log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x))^2*log (log(x)) - 2*I*pi*log(x)^2*log(-log(x))^2*log(log(x)) - 3*I*pi*log(x)*log( -log(x))^2*log(log(x))^2 - log(-log(-log(x))^2 - 4*log(-log(x)))*log(x)*lo g(-log(x))^2*log(log(x))^2 - log(x)^2*log(-log(x))^2*log(log(x))^2 - log(x )*log(-log(x))^2*log(log(x))^3 + 4*I*pi^3*log(x)*log(-log(x)) + 4*pi^2*log (-log(-log(x))^2 - 4*log(-log(x)))*log(x)*log(-log(x)) + 4*pi^2*log(x)^2*l og(-log(x)) + I*pi^3*log(-log(x))^2 + pi^2*log(-log(-log(x))^2 - 4*log(-lo g(x)))*log(-log(x))^2 + 5*pi^2*log(x)*log(-log(x))^2 - 4*I*pi*log(-log(...
Timed out. \[ \int \frac {4 \log \left (\frac {1}{x}\right )+4 \log \left (\frac {1}{x}\right ) \log (x)+2 \log (x) \log \left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-\log \left (\frac {1}{x}\right )-\log \left (\frac {1}{x}\right ) \log (x)\right ) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )+\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log \left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )}{\left (-4 \log \left (\frac {1}{x}\right ) \log (x)+\log \left (\frac {1}{x}\right ) \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right ) \log ^2\left (4 x \log (x)-x \log (x) \log ^2\left (e^2 \log \left (\frac {1}{x}\right )\right )\right )} \, dx=-\int \frac {4\,\ln \left (\frac {1}{x}\right )-{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\left (\ln \left (\frac {1}{x}\right )+\ln \left (\frac {1}{x}\right )\,\ln \left (x\right )\right )+4\,\ln \left (\frac {1}{x}\right )\,\ln \left (x\right )+2\,\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )\,\ln \left (x\right )-\ln \left (4\,x\,\ln \left (x\right )-x\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \left (x\right )\right )\,\left (4\,\ln \left (\frac {1}{x}\right )\,\ln \left (x\right )-\ln \left (\frac {1}{x}\right )\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \left (x\right )\right )}{{\ln \left (4\,x\,\ln \left (x\right )-x\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \left (x\right )\right )}^2\,\left (4\,\ln \left (\frac {1}{x}\right )\,\ln \left (x\right )-\ln \left (\frac {1}{x}\right )\,{\ln \left (\ln \left (\frac {1}{x}\right )\,{\mathrm {e}}^2\right )}^2\,\ln \left (x\right )\right )} \,d x \]
int(-(4*log(1/x) - log(log(1/x)*exp(2))^2*(log(1/x) + log(1/x)*log(x)) + 4 *log(1/x)*log(x) + 2*log(log(1/x)*exp(2))*log(x) - log(4*x*log(x) - x*log( log(1/x)*exp(2))^2*log(x))*(4*log(1/x)*log(x) - log(1/x)*log(log(1/x)*exp( 2))^2*log(x)))/(log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))^2*(4*log (1/x)*log(x) - log(1/x)*log(log(1/x)*exp(2))^2*log(x))),x)
-int((4*log(1/x) - log(log(1/x)*exp(2))^2*(log(1/x) + log(1/x)*log(x)) + 4 *log(1/x)*log(x) + 2*log(log(1/x)*exp(2))*log(x) - log(4*x*log(x) - x*log( log(1/x)*exp(2))^2*log(x))*(4*log(1/x)*log(x) - log(1/x)*log(log(1/x)*exp( 2))^2*log(x)))/(log(4*x*log(x) - x*log(log(1/x)*exp(2))^2*log(x))^2*(4*log (1/x)*log(x) - log(1/x)*log(log(1/x)*exp(2))^2*log(x))), x)