/ 2*x\ / 2 \
\x / 2*x | 1 2*x /1 \ 2*log(x) 4*(1 + log(x)) 2 |
x *x *|- -- + x *|- + 2*(1 + log(x))*log(x)| + -------- + -------------- + 4*(1 + log(x)) *log(x)|
| 2 \x / x x |
\ x /
$$x^{2 x} x^{x^{2 x}} \left(x^{2 x} \left(2 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + 4 \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{4 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{2 \log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)$$
/ 2*x\ / 3 2 \
\x / 2*x |2 6 4*x /1 \ 6*(1 + log(x)) 2*log(x) 3 12*(1 + log(x)) 2*x /1 \ / 1 2*log(x) 4*(1 + log(x)) 2 \ 12*(1 + log(x))*log(x)|
x *x *|-- + -- + x *|- + 2*(1 + log(x))*log(x)| - -------------- - -------- + 8*(1 + log(x)) *log(x) + ---------------- + 3*x *|- + 2*(1 + log(x))*log(x)|*|- -- + -------- + -------------- + 4*(1 + log(x)) *log(x)| + ----------------------|
| 3 2 \x / 2 2 x \x / | 2 x x | x |
\x x x x \ x / /
$$x^{2 x} x^{x^{2 x}} \left(x^{4 x} \left(2 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{2 x} \left(2 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(4 \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{4 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{2 \log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + 8 \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + \frac{12 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{12 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{6 \left(\log{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \log{\left(x \right)}}{x^{2}} + \frac{6}{x^{2}} + \frac{2}{x^{3}}\right)$$