\(\int \frac {-2 x^2 \log (x) \log (\frac {5 e^x \log (x)}{x})+e^{10} \log ^2(\frac {5 e^x \log (x)}{x}) (-32-16 x-2 x^2+(32-16 x-14 x^2-2 x^3) \log (x)+(-8 x-2 x^2) \log (x) \log (\frac {5 e^x \log (x)}{x}))+e^5 \log (\frac {5 e^x \log (x)}{x}) (8 x+2 x^2+(-8 x+6 x^2+2 x^3) \log (x)+(8 x+4 x^2) \log (x) \log (\frac {5 e^x \log (x)}{x}))}{x \log (x) \log (\frac {5 e^x \log (x)}{x})} \, dx\) [1611]

Optimal result

Integrand size = 172, antiderivative size = 28 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=3-\left (-x+e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )^2 \]

[Out]

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

Rubi [F]

\[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=\int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx \]

[In]

Int[(-2*x^2*Log[x]*Log[(5*E^x*Log[x])/x] + E^10*Log[(5*E^x*Log[x])/x]^2*(-32 - 16*x - 2*x^2 + (32 - 16*x - 14*
x^2 - 2*x^3)*Log[x] + (-8*x - 2*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]) + E^5*Log[(5*E^x*Log[x])/x]*(8*x + 2*x^2 +
(-8*x + 6*x^2 + 2*x^3)*Log[x] + (8*x + 4*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]))/(x*Log[x]*Log[(5*E^x*Log[x])/x]),
x]

[Out]

-8*E^5*x + 16*E^10*x + 8*E^5*(1 - 2*E^5)*x - x^2 + 3*E^5*x^2 + (E^5*(2 - 7*E^5)*x^2)/2 - 4*E^5*(1 - 2*E^5)*x^2
+ (2*E^5*x^3)/3 - (2*E^10*x^3)/9 - (E^5*(2 - 7*E^5)*x^3)/3 + (E^10*x^4)/6 + 2*E^5*ExpIntegralEi[2*Log[x]] - 1
6*E^10*ExpIntegralEi[2*Log[x]] - E^5*(2 - 7*E^5)*ExpIntegralEi[2*Log[x]] + (2*E^10*ExpIntegralEi[3*Log[x]])/3
+ 8*E^5*(1 - 2*E^5)*x*Log[(5*E^x*Log[x])/x] + E^5*(2 - 7*E^5)*x^2*Log[(5*E^x*Log[x])/x] - (2*E^10*x^3*Log[(5*E
^x*Log[x])/x])/3 + 8*E^5*LogIntegral[x] - 8*E^5*(1 - 2*E^5)*LogIntegral[x] + 16*E^10*x*LogIntegral[x] - 16*E^1
0*Log[x]*LogIntegral[x] - 16*E^10*Log[(5*E^x*Log[x])/x]*LogIntegral[x] + 32*E^10*Defer[Int][Log[(5*E^x*Log[x])
/x]/x, x] - 32*E^10*Defer[Int][Log[(5*E^x*Log[x])/x]/(x*Log[x]), x] - 2*E^10*Defer[Int][(x*Log[(5*E^x*Log[x])/
x])/Log[x], x] - 8*E^10*Defer[Int][Log[(5*E^x*Log[x])/x]^2, x] - 2*E^10*Defer[Int][x*Log[(5*E^x*Log[x])/x]^2,
x] + 16*E^10*Defer[Int][LogIntegral[x]/(x*Log[x]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx \\ & = 2 \int \frac {\left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx \\ & = 2 \int \left (\frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)}+\frac {e^5 \left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-e^{10} (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx \\ & = 2 \int \frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)} \, dx+\left (2 e^5\right ) \int \frac {\left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = 2 \int \left (-x+e^5 \left (-4+3 x+x^2\right )+\frac {e^5 (4+x)}{\log (x)}\right ) \, dx+\left (2 e^5\right ) \int \frac {\left (-e^5 (4+x)^2-\left (-2 x (2+x)+e^5 (-1+x) (4+x)^2\right ) \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int \left (4 \log ^2\left (\frac {5 e^x \log (x)}{x}\right )+x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx \\ & = -x^2+\left (2 e^5\right ) \int \left (-4+3 x+x^2\right ) \, dx+\left (2 e^5\right ) \int \frac {4+x}{\log (x)} \, dx+\left (2 e^5\right ) \int \left (4 \left (1-2 e^5\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )+\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x}+2 \left (1-\frac {7 e^5}{2}\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )-e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {8 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}-\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-\frac {e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = -8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+\left (2 e^5\right ) \int \left (\frac {4}{\log (x)}+\frac {x}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x^2 \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (16 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx+\left (2 e^5 \left (2-7 e^5\right )\right ) \int x \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (8 e^5 \left (1-2 e^5\right )\right ) \int \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = -8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\left (2 e^5\right ) \int \frac {x}{\log (x)} \, dx+\left (8 e^5\right ) \int \frac {1}{\log (x)} \, dx+\left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{3 \log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {(1+(-1+x) \log (x)) \operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{2 \log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \left (-1+x+\frac {1}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\left (2 e^5\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \left (\operatorname {LogIntegral}(x)-\frac {\operatorname {LogIntegral}(x)}{x}+\frac {\operatorname {LogIntegral}(x)}{x \log (x)}\right ) \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \frac {1}{\log (x)} \, dx \\ & = -8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left ((-1+x) x^2+\frac {x^2}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \operatorname {LogIntegral}(x) \, dx-\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x} \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int x \left (-1+x+\frac {1}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int (-1+x) x^2 \, dx+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left ((-1+x) x+\frac {x}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left (-x^2+x^3\right ) \, dx+\frac {1}{3} \left (2 e^{10}\right ) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int (-1+x) x \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x}{\log (x)} \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}+\frac {e^{10} x^4}{6}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+\frac {2}{3} e^{10} \operatorname {ExpIntegralEi}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left (-x+x^2\right ) \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right ) \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2+\frac {1}{2} e^5 \left (2-7 e^5\right ) x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}-\frac {1}{3} e^5 \left (2-7 e^5\right ) x^3+\frac {e^{10} x^4}{6}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))-e^5 \left (2-7 e^5\right ) \operatorname {ExpIntegralEi}(2 \log (x))+\frac {2}{3} e^{10} \operatorname {ExpIntegralEi}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(180\) vs. \(2(28)=56\).

Time = 0.69 (sec) , antiderivative size = 180, normalized size of antiderivative = 6.43 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-x^2+16 e^{10} x^2-16 e^{10} \log ^2\left (\frac {\log (x)}{x}\right )-32 e^{10} \log (x) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+32 e^{10} \log (\log (x)) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+8 e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )-32 e^{10} x \log \left (\frac {5 e^x \log (x)}{x}\right )+2 e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-8 e^{10} x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )-e^{10} x^2 \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \]

[In]

Integrate[(-2*x^2*Log[x]*Log[(5*E^x*Log[x])/x] + E^10*Log[(5*E^x*Log[x])/x]^2*(-32 - 16*x - 2*x^2 + (32 - 16*x
- 14*x^2 - 2*x^3)*Log[x] + (-8*x - 2*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]) + E^5*Log[(5*E^x*Log[x])/x]*(8*x + 2*
x^2 + (-8*x + 6*x^2 + 2*x^3)*Log[x] + (8*x + 4*x^2)*Log[x]*Log[(5*E^x*Log[x])/x]))/(x*Log[x]*Log[(5*E^x*Log[x]
)/x]),x]

[Out]

-x^2 + 16*E^10*x^2 - 16*E^10*Log[Log[x]/x]^2 - 32*E^10*Log[x]*(x + Log[Log[x]/x] - Log[(5*E^x*Log[x])/x]) + 32
*E^10*Log[Log[x]]*(x + Log[Log[x]/x] - Log[(5*E^x*Log[x])/x]) + 8*E^5*x*Log[(5*E^x*Log[x])/x] - 32*E^10*x*Log[
(5*E^x*Log[x])/x] + 2*E^5*x^2*Log[(5*E^x*Log[x])/x] - 8*E^10*x*Log[(5*E^x*Log[x])/x]^2 - E^10*x^2*Log[(5*E^x*L
og[x])/x]^2

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(185\) vs. \(2(28)=56\).

Time = 16.49 (sec) , antiderivative size = 186, normalized size of antiderivative = 6.64

method	result	size
parallelrisch	\(\frac {-\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10} x^{2}+2 \,{\mathrm e}^{\ln \left (\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )\right )+5} \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x^{2}-8 \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10} x -\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x^{2}+8 \,{\mathrm e}^{\ln \left (\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )\right )+5} \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x -16 \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10}}{\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2}}\)	\(186\)
risch	\(\text {Expression too large to display}\)	\(5910\)

[In]

int((((-2*x^2-8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(-2*x^3-14*x^2-16*x+32)*ln(x)-2*x^2-16*x-32)*exp(ln(ln(5*exp(x)*
ln(x)/x))+5)^2+((4*x^2+8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(2*x^3+6*x^2-8*x)*ln(x)+2*x^2+8*x)*exp(ln(ln(5*exp(x)*l
n(x)/x))+5)-2*x^2*ln(x)*ln(5*exp(x)*ln(x)/x))/x/ln(x)/ln(5*exp(x)*ln(x)/x),x,method=_RETURNVERBOSE)

[Out]

(-exp(ln(ln(5*exp(x)*ln(x)/x))+5)^2*ln(5*exp(x)*ln(x)/x)^2*x^2+2*exp(ln(ln(5*exp(x)*ln(x)/x))+5)*ln(5*exp(x)*l
n(x)/x)^2*x^2-8*exp(ln(ln(5*exp(x)*ln(x)/x))+5)^2*ln(5*exp(x)*ln(x)/x)^2*x-ln(5*exp(x)*ln(x)/x)^2*x^2+8*exp(ln
(ln(5*exp(x)*ln(x)/x))+5)*ln(5*exp(x)*ln(x)/x)^2*x-16*exp(ln(ln(5*exp(x)*ln(x)/x))+5)^2*ln(5*exp(x)*ln(x)/x)^2
)/ln(5*exp(x)*ln(x)/x)^2

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-{\left (x^{2} + 8 \, x + 16\right )} e^{10} \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )^{2} + 2 \, {\left (x^{2} + 4 \, x\right )} e^{5} \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) - x^{2} \]

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="fricas")

[Out]

-(x^2 + 8*x + 16)*e^10*log(5*e^x*log(x)/x)^2 + 2*(x^2 + 4*x)*e^5*log(5*e^x*log(x)/x) - x^2

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (22) = 44\).

Time = 0.34 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=- x^{2} + \left (2 x^{2} e^{5} + 8 x e^{5}\right ) \log {\left (\frac {5 e^{x} \log {\left (x \right )}}{x} \right )} + \left (- x^{2} e^{10} - 8 x e^{10} - 16 e^{10}\right ) \log {\left (\frac {5 e^{x} \log {\left (x \right )}}{x} \right )}^{2} \]

[In]

integrate((((-2*x**2-8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(-2*x**3-14*x**2-16*x+32)*ln(x)-2*x**2-16*x-32)*exp(ln(ln
(5*exp(x)*ln(x)/x))+5)**2+((4*x**2+8*x)*ln(x)*ln(5*exp(x)*ln(x)/x)+(2*x**3+6*x**2-8*x)*ln(x)+2*x**2+8*x)*exp(l
n(ln(5*exp(x)*ln(x)/x))+5)-2*x**2*ln(x)*ln(5*exp(x)*ln(x)/x))/x/ln(x)/ln(5*exp(x)*ln(x)/x),x)

[Out]

-x**2 + (2*x**2*exp(5) + 8*x*exp(5))*log(5*exp(x)*log(x)/x) + (-x**2*exp(10) - 8*x*exp(10) - 16*exp(10))*log(5
*exp(x)*log(x)/x)**2

Maxima [F]

\[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=\int { -\frac {2 \, {\left (x^{2} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + {\left ({\left (x^{2} + 4 \, x\right )} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + x^{2} + {\left (x^{3} + 7 \, x^{2} + 8 \, x - 16\right )} \log \left (x\right ) + 8 \, x + 16\right )} e^{\left (2 \, \log \left (\log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )\right ) + 10\right )} - {\left (2 \, {\left (x^{2} + 2 \, x\right )} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + x^{2} + {\left (x^{3} + 3 \, x^{2} - 4 \, x\right )} \log \left (x\right ) + 4 \, x\right )} e^{\left (\log \left (\log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )\right ) + 5\right )}\right )}}{x \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )} \,d x } \]

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="maxima")

[Out]

-x^4*e^10 - 2/3*(3*(log(5) + 4)*e^10 - 2*e^5)*x^3 + 2/3*x^3*e^5 - ((log(5)^2 + 16*log(5) + 16)*e^10 - (2*log(5
) + 5)*e^5)*x^2 + 3*x^2*e^5 - (x^2*e^10 + 8*x*e^10 + 16*e^10)*log(x)^2 - (x^2*e^10 + 8*x*e^10 + 16*e^10)*log(l
og(x))^2 - 8*((log(5)^2 + 4*log(5))*e^10 - (log(5) + 1)*e^5)*x - x^2 - 8*x*e^5 + 2*Ei(2*log(x))*e^5 + 8*Ei(log
(x))*e^5 + 2*(x^3*e^10 + ((log(5) + 8)*e^10 - e^5)*x^2 + 4*(2*(log(5) + 2)*e^10 - e^5)*x + 16*e^10*log(5))*log
(x) - 2*(x^3*e^10 + ((log(5) + 8)*e^10 - e^5)*x^2 + 4*(2*(log(5) + 2)*e^10 - e^5)*x - (x^2*e^10 + 8*x*e^10 + 1
6*e^10)*log(x))*log(log(x)) - 2*integrate((x^2*e^5 + 4*x*e^5 + 16*e^10*log(5))/(x*log(x)), x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 338 vs. \(2 (28) = 56\).

Time = 0.35 (sec) , antiderivative size = 338, normalized size of antiderivative = 12.07 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-x^{4} e^{10} - 2 \, x^{3} e^{10} \log \left (5\right ) - x^{2} e^{10} \log \left (5\right )^{2} + 2 \, x^{3} e^{10} \log \left (x\right ) + 2 \, x^{2} e^{10} \log \left (5\right ) \log \left (x\right ) - x^{2} e^{10} \log \left (x\right )^{2} - 2 \, x^{3} e^{10} \log \left (\log \left (x\right )\right ) - 2 \, x^{2} e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 2 \, x^{2} e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - x^{2} e^{10} \log \left (\log \left (x\right )\right )^{2} - 8 \, x^{3} e^{10} + 2 \, x^{3} e^{5} - 16 \, x^{2} e^{10} \log \left (5\right ) + 2 \, x^{2} e^{5} \log \left (5\right ) - 8 \, x e^{10} \log \left (5\right )^{2} + 16 \, x^{2} e^{10} \log \left (x\right ) - 2 \, x^{2} e^{5} \log \left (x\right ) + 16 \, x e^{10} \log \left (5\right ) \log \left (x\right ) - 8 \, x e^{10} \log \left (x\right )^{2} - 16 \, x^{2} e^{10} \log \left (\log \left (x\right )\right ) + 2 \, x^{2} e^{5} \log \left (\log \left (x\right )\right ) - 16 \, x e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 16 \, x e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 8 \, x e^{10} \log \left (\log \left (x\right )\right )^{2} - 16 \, x^{2} e^{10} + 8 \, x^{2} e^{5} - 32 \, x e^{10} \log \left (5\right ) + 8 \, x e^{5} \log \left (5\right ) + 32 \, x e^{10} \log \left (x\right ) - 8 \, x e^{5} \log \left (x\right ) + 32 \, e^{10} \log \left (5\right ) \log \left (x\right ) - 16 \, e^{10} \log \left (x\right )^{2} - 32 \, x e^{10} \log \left (\log \left (x\right )\right ) + 8 \, x e^{5} \log \left (\log \left (x\right )\right ) - 32 \, e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 32 \, e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 16 \, e^{10} \log \left (\log \left (x\right )\right )^{2} - x^{2} \]

[In]

integrate((((-2*x^2-8*x)*log(x)*log(5*exp(x)*log(x)/x)+(-2*x^3-14*x^2-16*x+32)*log(x)-2*x^2-16*x-32)*exp(log(l
og(5*exp(x)*log(x)/x))+5)^2+((4*x^2+8*x)*log(x)*log(5*exp(x)*log(x)/x)+(2*x^3+6*x^2-8*x)*log(x)+2*x^2+8*x)*exp
(log(log(5*exp(x)*log(x)/x))+5)-2*x^2*log(x)*log(5*exp(x)*log(x)/x))/x/log(x)/log(5*exp(x)*log(x)/x),x, algori
thm="giac")

[Out]

-x^4*e^10 - 2*x^3*e^10*log(5) - x^2*e^10*log(5)^2 + 2*x^3*e^10*log(x) + 2*x^2*e^10*log(5)*log(x) - x^2*e^10*lo
g(x)^2 - 2*x^3*e^10*log(log(x)) - 2*x^2*e^10*log(5)*log(log(x)) + 2*x^2*e^10*log(x)*log(log(x)) - x^2*e^10*log
(log(x))^2 - 8*x^3*e^10 + 2*x^3*e^5 - 16*x^2*e^10*log(5) + 2*x^2*e^5*log(5) - 8*x*e^10*log(5)^2 + 16*x^2*e^10*
log(x) - 2*x^2*e^5*log(x) + 16*x*e^10*log(5)*log(x) - 8*x*e^10*log(x)^2 - 16*x^2*e^10*log(log(x)) + 2*x^2*e^5*
log(log(x)) - 16*x*e^10*log(5)*log(log(x)) + 16*x*e^10*log(x)*log(log(x)) - 8*x*e^10*log(log(x))^2 - 16*x^2*e^
10 + 8*x^2*e^5 - 32*x*e^10*log(5) + 8*x*e^5*log(5) + 32*x*e^10*log(x) - 8*x*e^5*log(x) + 32*e^10*log(5)*log(x)
- 16*e^10*log(x)^2 - 32*x*e^10*log(log(x)) + 8*x*e^5*log(log(x)) - 32*e^10*log(5)*log(log(x)) + 32*e^10*log(x
)*log(log(x)) - 16*e^10*log(log(x))^2 - x^2

Mupad [B] (verification not implemented)

Time = 9.40 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-{\left (4\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \left (x\right )}{x}\right )\,{\mathrm {e}}^5-x+x\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \left (x\right )}{x}\right )\,{\mathrm {e}}^5\right )}^2 \]

[In]

int(-(exp(2*log(log((5*exp(x)*log(x))/x)) + 10)*(16*x + 2*x^2 + log(x)*(16*x + 14*x^2 + 2*x^3 - 32) + log((5*e
xp(x)*log(x))/x)*log(x)*(8*x + 2*x^2) + 32) - exp(log(log((5*exp(x)*log(x))/x)) + 5)*(8*x + 2*x^2 + log(x)*(6*
x^2 - 8*x + 2*x^3) + log((5*exp(x)*log(x))/x)*log(x)*(8*x + 4*x^2)) + 2*x^2*log((5*exp(x)*log(x))/x)*log(x))/(
x*log((5*exp(x)*log(x))/x)*log(x)),x)

[Out]

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