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David H
  • Member for 9 years, 5 months
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  • The South
28 votes
4 answers
915 views

Integrals of integer powers of dilogarithm function

28 votes
1 answer
999 views

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

24 votes
2 answers
555 views

Definite integral of arcsine over square-root of quadratic

18 votes
3 answers
567 views

Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

17 votes
3 answers
2k views

How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

12 votes
3 answers
1k views

How to demonstrate the equality of these integral representations of $\pi$?

11 votes
2 answers
2k views

Closed form for integral of integer powers of Sinc function

10 votes
4 answers
576 views

Evaluation of a dilogarithmic integral

9 votes
2 answers
245 views

Indefinite integral typo in Gradshteĭn: reciprocal square-root of sixth degree polynomial

8 votes
2 answers
329 views

Closed form for $\int z^n\ln{(z)}\ln{(1-z)}\,\mathrm{d}z$?

8 votes
2 answers
451 views

Closed form for integral of inverse hyperbolic function in terms of ${_4F_3}$

8 votes
1 answer
274 views

Another polylog integral

7 votes
1 answer
255 views

Challenging definite integral of hypergeometric functions

7 votes
2 answers
290 views

Prove: $\int_{0}^{1}\frac{\ln{x}\,\mathrm{d}x}{\sqrt[3]{x(1-x^2)^2}}\stackrel{?}{=}-\frac18\left[\Gamma{\left(\frac13\right)}\right]^3$

7 votes
3 answers
683 views

Proofs without words of some well-known historical values of $\pi$?

6 votes
2 answers
370 views

Prove this polylogarithmic integral has the stated closed form value

6 votes
3 answers
589 views

Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function

5 votes
0 answers
152 views

Verifying closed form evaluation of an Ising-class multiple integral

5 votes
1 answer
260 views

Seeking closed-form solution to $\sum_{n=1}^{\infty}\frac{\log{(1+n)}}{(1+n)^{\alpha}-1}$

5 votes
1 answer
351 views

Simplifying a certain polylogarithmic sum in two variables

5 votes
1 answer
793 views

Simplifying real part of hypergeometric function with complex parameters

4 votes
1 answer
439 views

Extending the rationals using exponentiation

4 votes
1 answer
100 views

Closed form evaluation of a trigonometric integral in terms of polylogarithms

3 votes
1 answer
139 views

Factoring the quartic $\left(x^{2}+x-1\right)\left(x^{2}+2x-1\right)-2sx\left(2x-1\right)^{2}$

3 votes
1 answer
406 views

Evaluating a double integral of a complicated rational function

3 votes
1 answer
146 views

Closed form of a trigonometric integral sought

3 votes
1 answer
183 views

Evaluating a logarithmic integral in terms of trilogarithms

2 votes
1 answer
1k views

Need help understanding a certain vector integral identity (Stokes' theorem corollary)

2 votes
0 answers
174 views

Reduction of a type of elliptic integral to Legendre normal form

2 votes
2 answers
155 views

Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)