All Questions
3
questions
3
votes
0
answers
291
views
Evaluate $\int_{1}^{\infty}\frac{\operatorname{Li}_3(-x)\ln(x-1)}{1+x^2}\text{d}x$
Using $$
\operatorname{Li}_3(-x)
=-\frac{x}{2}\int_{0}^{1}\frac{\ln^2t}{1+tx}
\text{d}t
$$
It might be
$$
-\frac{1}{2}\int_{0}^{1}\ln^2t
\int_{1}^{\infty}\frac{x\ln(x-1)}{(1+tx)(1+x^2)}\text{d}x\text{...
- 5,370
3
votes
1
answer
226
views
The indefinite integral $\int\frac{\operatorname{Li}_2(x)}{1+\sqrt{x}}\,dx$: what is the strategy to get such indefinite integral
Here there is an integral that I've found playing with Wolfram Alpha online calculator (thus to me is a curiosity that it has indefinite integral) $$\int\frac{\operatorname{Li}_2(x)}{1+\sqrt{x}}\,dx,\...
user243301
1
vote
1
answer
712
views
Integration of a polylogarithm: Is this function known?
I would like to integrate a polylogarithm of a given order
$$\int dx \mbox{Li}_{n-1}(x)$$
suppose that the order is $n\le 0$ and $x\in(-\infty,0]$, so the function is bounded. I know that it can be ...
- 1,742