All Questions
Tagged with polylogarithm indefinite-integrals
2
questions with no upvoted or accepted answers
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
$$
-\frac{1}{2}\int_{0}^{1}\ln^2t
\int_{1}^{\infty}\frac{x\ln(x-1)}{(1+tx)(1+x^2)}\text{d}x\text{...
- 5,370
1
vote
0
answers
117
views
Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$
In my partial answer to this question: Integral involving polylogarithm and an exponential, I arrive at the integral
$$ \int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds , ~~~~ (\ast) $$
where $a \in ...
- 753