Integrand size = 286, antiderivative size = 28 \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\log \left (5-x+\log (x)+\frac {x}{\log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}\right ) \] Output:
ln(5+x/ln(ln(ln(2/x))+ln(5)-x^2)+ln(x)-x)
\[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx \] Input:
Integrate[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*L og[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]] + ((-x^2 + x^3 + (1 - x)* Log[5])*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log [Log[2/x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]] )*Log[-x^2 + Log[5] + Log[Log[2/x]]] + ((-5*x^3 + x^4 + (5*x - x^2)*Log[5] )*Log[2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x] + x *Log[2/x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^2),x]
Output:
Integrate[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*L og[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]] + ((-x^2 + x^3 + (1 - x)* Log[5])*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log [Log[2/x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]] )*Log[-x^2 + Log[5] + Log[Log[2/x]]] + ((-5*x^3 + x^4 + (5*x - x^2)*Log[5] )*Log[2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x] + x *Log[2/x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^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.
\(\displaystyle \int \frac {2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (x^3-x^2+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\log \left (\frac {2}{x}\right )\right ) \log \left (\frac {2}{x}\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+\left (\left (x \log (5)-x^3\right ) \log \left (\frac {2}{x}\right )+x \log \left (\log \left (\frac {2}{x}\right )\right ) \log \left (\frac {2}{x}\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x}{\left (x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )+\left (x^2 \log (5)-x^4\right ) \log \left (\frac {2}{x}\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+\left (\left (x \log (5)-x^3\right ) \log (x) \log \left (\frac {2}{x}\right )+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log (x) \log \left (\frac {2}{x}\right )\right ) \log \left (\log \left (\frac {2}{x}\right )\right )+\left (x^4-5 x^3+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )} \, dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {-\log \left (\frac {2}{x}\right ) \left (2 x^3+(x-1) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )+x \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )-x}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right ) \left (x-(x-\log (x)-5) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-2 x^2 \log \left (\frac {2}{x}\right )-1}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )}+\frac {4 x^2+x^2 \log (x)+x \log \left (\log \left (\frac {2}{x}\right )\right )-x \log \left (5 \log \left (\frac {2}{x}\right )\right )+x \log (5)-\log (5) \log (x)-\log (x) \log \left (\log \left (\frac {2}{x}\right )\right )-5 \log \left (\log \left (\frac {2}{x}\right )\right )+\log \left (5 \log \left (\frac {2}{x}\right )\right )-5 \log (5)}{(x-\log (x)-5) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {\left (2 x^2 \log \left (\frac {2}{x}\right )+1\right ) (x-\log (x)-5)}{x \log \left (\frac {2}{x}\right ) \left (x^2-\log \left (5 \log \left (\frac {2}{x}\right )\right )\right ) \left (x \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-\log (x) \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-5 \log \left (-x^2+\log \left (\log \left (\frac {2}{x}\right )\right )+\log (5)\right )-x\right )}+\frac {x-1}{x (x-\log (x)-5)}\right )dx\) |
Input:
Int[(x + 2*x^3*Log[2/x] + ((-x^3 + x*Log[5])*Log[2/x] + x*Log[2/x]*Log[Log [2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]] + ((-x^2 + x^3 + (1 - x)*Log[5] )*Log[2/x] + (1 - x)*Log[2/x]*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2 /x]]]^2)/(((-x^4 + x^2*Log[5])*Log[2/x] + x^2*Log[2/x]*Log[Log[2/x]])*Log[ -x^2 + Log[5] + Log[Log[2/x]]] + ((-5*x^3 + x^4 + (5*x - x^2)*Log[5])*Log[ 2/x] + (-x^3 + x*Log[5])*Log[2/x]*Log[x] + ((5*x - x^2)*Log[2/x] + x*Log[2 /x]*Log[x])*Log[Log[2/x]])*Log[-x^2 + Log[5] + Log[Log[2/x]]]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(28)=56\).
Time = 0.71 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14
\[\ln \left (x -\ln \left (x \right )-5\right )+\ln \left (\ln \left (\ln \left (\ln \left (2\right )-\ln \left (x \right )\right )+\ln \left (5\right )-x^{2}\right )+\frac {x}{\ln \left (x \right )-x +5}\right )-\ln \left (\ln \left (\ln \left (\ln \left (2\right )-\ln \left (x \right )\right )+\ln \left (5\right )-x^{2}\right )\right )\]
Input:
int((((1-x)*ln(2/x)*ln(ln(2/x))+((1-x)*ln(5)+x^3-x^2)*ln(2/x))*ln(ln(ln(2/ x))+ln(5)-x^2)^2+(x*ln(2/x)*ln(ln(2/x))+(x*ln(5)-x^3)*ln(2/x))*ln(ln(ln(2/ x))+ln(5)-x^2)+2*x^3*ln(2/x)+x)/(((x*ln(2/x)*ln(x)+(-x^2+5*x)*ln(2/x))*ln( ln(2/x))+(x*ln(5)-x^3)*ln(2/x)*ln(x)+((-x^2+5*x)*ln(5)+x^4-5*x^3)*ln(2/x)) *ln(ln(ln(2/x))+ln(5)-x^2)^2+(x^2*ln(2/x)*ln(ln(2/x))+(x^2*ln(5)-x^4)*ln(2 /x))*ln(ln(ln(2/x))+ln(5)-x^2)),x)
Output:
ln(x-ln(x)-5)+ln(ln(ln(ln(2)-ln(x))+ln(5)-x^2)+x/(ln(x)-x+5))-ln(ln(ln(ln( 2)-ln(x))+ln(5)-x^2))
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\log \left (x - \log \left (2\right ) + \log \left (\frac {2}{x}\right ) - 5\right ) + \log \left (\frac {{\left (x - \log \left (2\right ) + \log \left (\frac {2}{x}\right ) - 5\right )} \log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (\frac {2}{x}\right )\right )\right ) - x}{x - \log \left (2\right ) + \log \left (\frac {2}{x}\right ) - 5}\right ) - \log \left (\log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (\frac {2}{x}\right )\right )\right )\right ) \] Input:
integrate((((1-x)*log(2/x)*log(log(2/x))+((1-x)*log(5)+x^3-x^2)*log(2/x))* log(log(log(2/x))+log(5)-x^2)^2+(x*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*l og(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)*log (x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x ^2+5*x)*log(5)+x^4-5*x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*l og(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+log(5)- x^2)),x, algorithm="fricas")
Output:
log(x - log(2) + log(2/x) - 5) + log(((x - log(2) + log(2/x) - 5)*log(-x^2 + log(5) + log(log(2/x))) - x)/(x - log(2) + log(2/x) - 5)) - log(log(-x^ 2 + log(5) + log(log(2/x))))
Timed out. \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\text {Timed out} \] Input:
integrate((((1-x)*ln(2/x)*ln(ln(2/x))+((1-x)*ln(5)+x**3-x**2)*ln(2/x))*ln( ln(ln(2/x))+ln(5)-x**2)**2+(x*ln(2/x)*ln(ln(2/x))+(x*ln(5)-x**3)*ln(2/x))* ln(ln(ln(2/x))+ln(5)-x**2)+2*x**3*ln(2/x)+x)/(((x*ln(2/x)*ln(x)+(-x**2+5*x )*ln(2/x))*ln(ln(2/x))+(x*ln(5)-x**3)*ln(2/x)*ln(x)+((-x**2+5*x)*ln(5)+x** 4-5*x**3)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x**2)**2+(x**2*ln(2/x)*ln(ln(2/x)) +(x**2*ln(5)-x**4)*ln(2/x))*ln(ln(ln(2/x))+ln(5)-x**2)),x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (28) = 56\).
Time = 0.21 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.46 \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\log \left (-x + \log \left (x\right ) + 5\right ) + \log \left (\frac {{\left (x - \log \left (x\right ) - 5\right )} \log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right ) - x}{x - \log \left (x\right ) - 5}\right ) - \log \left (\log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right )\right ) \] Input:
integrate((((1-x)*log(2/x)*log(log(2/x))+((1-x)*log(5)+x^3-x^2)*log(2/x))* log(log(log(2/x))+log(5)-x^2)^2+(x*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*l og(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)*log (x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x ^2+5*x)*log(5)+x^4-5*x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*l og(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+log(5)- x^2)),x, algorithm="maxima")
Output:
log(-x + log(x) + 5) + log(((x - log(x) - 5)*log(-x^2 + log(5) + log(log(2 ) - log(x))) - x)/(x - log(x) - 5)) - log(log(-x^2 + log(5) + log(log(2) - log(x))))
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (28) = 56\).
Time = 0.41 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\log \left (x \log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right ) - \log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right ) \log \left (x\right ) - x - 5 \, \log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right )\right ) - \log \left (\log \left (-x^{2} + \log \left (5\right ) + \log \left (\log \left (2\right ) - \log \left (x\right )\right )\right )\right ) \] Input:
integrate((((1-x)*log(2/x)*log(log(2/x))+((1-x)*log(5)+x^3-x^2)*log(2/x))* log(log(log(2/x))+log(5)-x^2)^2+(x*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*l og(2/x))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)*log (x)+(-x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x ^2+5*x)*log(5)+x^4-5*x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*l og(2/x)*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+log(5)- x^2)),x, algorithm="giac")
Output:
log(x*log(-x^2 + log(5) + log(log(2) - log(x))) - log(-x^2 + log(5) + log( log(2) - log(x)))*log(x) - x - 5*log(-x^2 + log(5) + log(log(2) - log(x))) ) - log(log(-x^2 + log(5) + log(log(2) - log(x))))
Timed out. \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=\int \frac {x-{\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \left (5\right )-x^2\right )}^2\,\left (\ln \left (\frac {2}{x}\right )\,\left (\ln \left (5\right )\,\left (x-1\right )+x^2-x^3\right )+\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\,\left (x-1\right )\right )+\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \left (5\right )-x^2\right )\,\left (\ln \left (\frac {2}{x}\right )\,\left (x\,\ln \left (5\right )-x^3\right )+x\,\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\right )+2\,x^3\,\ln \left (\frac {2}{x}\right )}{\left (\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\left (\ln \left (\frac {2}{x}\right )\,\left (5\,x-x^2\right )+x\,\ln \left (\frac {2}{x}\right )\,\ln \left (x\right )\right )+\ln \left (\frac {2}{x}\right )\,\left (\ln \left (5\right )\,\left (5\,x-x^2\right )-5\,x^3+x^4\right )+\ln \left (\frac {2}{x}\right )\,\ln \left (x\right )\,\left (x\,\ln \left (5\right )-x^3\right )\right )\,{\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \left (5\right )-x^2\right )}^2+\left (\ln \left (\frac {2}{x}\right )\,\left (x^2\,\ln \left (5\right )-x^4\right )+x^2\,\ln \left (\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\frac {2}{x}\right )\right )\,\ln \left (\ln \left (\ln \left (\frac {2}{x}\right )\right )+\ln \left (5\right )-x^2\right )} \,d x \] Input:
int((x - log(log(log(2/x)) + log(5) - x^2)^2*(log(2/x)*(log(5)*(x - 1) + x ^2 - x^3) + log(log(2/x))*log(2/x)*(x - 1)) + log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x*log(5) - x^3) + x*log(log(2/x))*log(2/x)) + 2*x^3*log(2 /x))/(log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x^2*log(5) - x^4) + x^2 *log(log(2/x))*log(2/x)) + log(log(log(2/x)) + log(5) - x^2)^2*(log(log(2/ x))*(log(2/x)*(5*x - x^2) + x*log(2/x)*log(x)) + log(2/x)*(log(5)*(5*x - x ^2) - 5*x^3 + x^4) + log(2/x)*log(x)*(x*log(5) - x^3))),x)
Output:
int((x - log(log(log(2/x)) + log(5) - x^2)^2*(log(2/x)*(log(5)*(x - 1) + x ^2 - x^3) + log(log(2/x))*log(2/x)*(x - 1)) + log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x*log(5) - x^3) + x*log(log(2/x))*log(2/x)) + 2*x^3*log(2 /x))/(log(log(log(2/x)) + log(5) - x^2)*(log(2/x)*(x^2*log(5) - x^4) + x^2 *log(log(2/x))*log(2/x)) + log(log(log(2/x)) + log(5) - x^2)^2*(log(log(2/ x))*(log(2/x)*(5*x - x^2) + x*log(2/x)*log(x)) + log(2/x)*(log(5)*(5*x - x ^2) - 5*x^3 + x^4) + log(2/x)*log(x)*(x*log(5) - x^3))), x)
Time = 0.21 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82 \[ \int \frac {x+2 x^3 \log \left (\frac {2}{x}\right )+\left (\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-x^2+x^3+(1-x) \log (5)\right ) \log \left (\frac {2}{x}\right )+(1-x) \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )}{\left (\left (-x^4+x^2 \log (5)\right ) \log \left (\frac {2}{x}\right )+x^2 \log \left (\frac {2}{x}\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log \left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )+\left (\left (-5 x^3+x^4+\left (5 x-x^2\right ) \log (5)\right ) \log \left (\frac {2}{x}\right )+\left (-x^3+x \log (5)\right ) \log \left (\frac {2}{x}\right ) \log (x)+\left (\left (5 x-x^2\right ) \log \left (\frac {2}{x}\right )+x \log \left (\frac {2}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {2}{x}\right )\right )\right ) \log ^2\left (-x^2+\log (5)+\log \left (\log \left (\frac {2}{x}\right )\right )\right )} \, dx=-\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\frac {2}{x}\right )\right )+\mathrm {log}\left (5\right )-x^{2}\right )\right )+\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\frac {2}{x}\right )\right )+\mathrm {log}\left (5\right )-x^{2}\right ) \mathrm {log}\left (x \right )-\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\frac {2}{x}\right )\right )+\mathrm {log}\left (5\right )-x^{2}\right ) x +5 \,\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\frac {2}{x}\right )\right )+\mathrm {log}\left (5\right )-x^{2}\right )+x \right ) \] Input:
int((((1-x)*log(2/x)*log(log(2/x))+((1-x)*log(5)+x^3-x^2)*log(2/x))*log(lo g(log(2/x))+log(5)-x^2)^2+(x*log(2/x)*log(log(2/x))+(x*log(5)-x^3)*log(2/x ))*log(log(log(2/x))+log(5)-x^2)+2*x^3*log(2/x)+x)/(((x*log(2/x)*log(x)+(- x^2+5*x)*log(2/x))*log(log(2/x))+(x*log(5)-x^3)*log(2/x)*log(x)+((-x^2+5*x )*log(5)+x^4-5*x^3)*log(2/x))*log(log(log(2/x))+log(5)-x^2)^2+(x^2*log(2/x )*log(log(2/x))+(x^2*log(5)-x^4)*log(2/x))*log(log(log(2/x))+log(5)-x^2)), x)
Output:
- log(log(log(log(2/x)) + log(5) - x**2)) + log(log(log(log(2/x)) + log(5 ) - x**2)*log(x) - log(log(log(2/x)) + log(5) - x**2)*x + 5*log(log(log(2/ x)) + log(5) - x**2) + x)