Интеграл (log(1+x/5))/x (dx)
Решение
1
/
|
| / x\
| log|1 + -|
| \ 5/
| ---------- dx
| x
|
/
0
$$\int_{0}^{1} \frac{1}{x} \log{\left (\frac{x}{5} + 1 \right )}\, dx$$
1
/
|
| / x\
| log|1 + -| / pi*I\
| \ 5/ | e |
| ---------- dx = -polylog|2, -----|
| x \ 5 /
|
/
0
$$\log \left(-{{1}\over{5}}\right)\,\log \left({{6}\over{5}}\right)+
{\it li}_{2}({{6}\over{5}})-{{\pi^2}\over{6}}$$