Question

Evaluate $\int_{0}^{1} \frac{\left[\rm{Li}_2\left(\frac{1}{2} \right)-\rm{Li}_2\left(\frac{1 + x}{2}\right)\right]\ln( 1 - x)}{1 + x}\,dx$

score 241 · Answer 1 · 2026-03-29 08:45:07

241

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Evaluate $\int_{0}^{1} \frac{\left[\rm{Li}_2\left(\frac{1}{2} \right)-\rm{Li}_2\left(\frac{1 + x}{2}\right)\right]\ln( 1 - x)}{1 + x}\,dx$

Published on 29 Mar 2026 - 8:45

score 752 · Answer 2 · 2014-10-12 13:53:24

752

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score 805 · Answer 3 · 2014-10-13 18:19:16

805

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2.1k

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316

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score 666 · Answer 7 · 2026-03-29 12:05:22

666

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score 279 · Answer 8 · 2026-03-28 18:16:58

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score 459 · Answer 9 · 2026-03-28 02:42:56

459

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score 465 · Answer 13 · 2026-03-26 02:47:50

465

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score 914 · Answer 14 · 2026-03-26 02:47:36

914

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score 590 · Answer 15 · 2026-03-28 20:14:27

590

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List Question

Evaluate $\int_{0}^{1} \frac{\left[\rm{Li}_2\left(\frac{1}{2} \right)-\rm{Li}_2\left(\frac{1 + x}{2}\right)\right]\ln( 1 - x)}{1 + x}\,dx$

How can one derive Stokes lines of the Stokes phenomenon of asymptotics from a differential equation?

Derivatives and Integrals of Summations

Extremely tough indefinite integral

octagonal number theorem $q$-Pochhammer symbol expression

How prime numbers are related to special functions?

Closed-form of $\int_0^1 B_n(x)\psi(x+1)\,dx$

Non-recursive closed-form of the coefficients of Taylor series of the reciprocal gamma function

Closed-form of the sequence ${_2F_1}\left(\begin{array}c\tfrac12,-n\\\tfrac32\end{array}\middle|\,\frac{1}{2}\right)$

Do the incomplete gamma functions have reflection formulas?

Closed-form of a special value dilogarithm identity

Evaluating a series of hypergeometric functions

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

Closed-form of $\int_0^1 \operatorname{Li}_3^3(x)\,dx$ and $\int_0^1 \operatorname{Li}_3^4(x)\,dx$

Closed-form of $\int_0^1 \left(\ln \Gamma(x)\right)^3\,dx$

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