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Is there an analytic solution to $\int_a^b \frac{\arctan(A+Bt)}{C^2 + (t-Z)^2}dt$?
Is there a sensible analytic solution to the following integral: $$\int_a^b \frac{\arctan(A+Bt)}{C^2 + (t-Z)^2}dt$$ where all constants are real and $C>0$.
This integral is part of the third term ...
- 31
11
votes
2
answers
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How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$
How to tackle
$$I=\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx\ ?$$
This integral came up while I was working on finding $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$.
First attempt: By ...
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29
votes
4
answers
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Yet another log-sin integral $\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\sin x)\,dx$
There has been much interest to various log-trig integrals on this site (e.g. see [1][2][3][4][5][6][7][8][9]).
Here is another one I'm trying to solve:
$$\int\limits_0^{\pi/3}\log(1+\sin x)\log(1-\...
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