All Questions
5
questions
3
votes
1
answer
244
views
How to solve $\int\frac{x\arctan x}{x^4+1}dx$ in a practical way
I need to evaluate the following indefinite integral for some other definite integral
$$\int\frac{x\arctan x}{x^4+1}dx$$
I found that
$$\int_o^\infty\arctan{(e^{-x})}\arctan{(e^{-2x})}dx=\frac{\pi G}{...
- 2,370
1
vote
0
answers
117
views
Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$
In my partial answer to this question: Integral involving polylogarithm and an exponential, I arrive at the integral
$$ \int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds , ~~~~ (\ast) $$
where $a \in ...
- 753
5
votes
1
answer
180
views
Is a closed form possible for $\int\frac{\text{Li}_2(x)^2}{x}dx$?
Can $\,\displaystyle\int\frac{\text{Li}_2(x)^2}{x}dx\,$ be calculated
by a sum/term of polylogarithm functions and the natural logarithm and polynomials (“closed form”) ?
For the special case $\,\...
- 11.6k
8
votes
2
answers
392
views
Closed form for $\int z^n\ln{(z)}\ln{(1-z)}\,\mathrm{d}z$?
Problem. Find an anti-derivative for the following indefinite integral, where $n$ is a non-negative integer:
$$\int z^n\ln{\left(z\right)}\ln{\left(1-z\right)}\,\mathrm{d}z=~???$$
My attempt:
...
- 30.7k
4
votes
3
answers
270
views
Tough quadrilogarithm integral
Solve the follolwing definite integral
$$\int \frac{\operatorname{Li}_4(z)}{1-z}\, dz$$
It is easy for lower powers!
- 14.4k