72 Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$ 41 Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$ 26 Why do some mathematical ideas seem counter-intuitive? 23 Distance between two points in spherical coordinates 22 A closed form for a lot of integrals on the logarithm

### Reputation (22,394)

 +5 Evaluating a certain integral which generalizes the ${_3F_2}$ hypergeometric function +10 A possible dilogarithm identity? +30 An incorrect answer for an integral +10 Finding the inverse of $f(x)=|x|-2$

### Questions (30)

 27 Integrals of integer powers of dilogarithm function 26 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 25 Definite integral of arcsine over square-root of quadratic 17 Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}$ 17 How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

### Tags (170)

 874 integration × 245 204 sequences-and-series × 54 723 calculus × 184 180 hypergeometric-function × 20 687 definite-integrals × 158 147 improper-integrals × 36 243 closed-form × 43 120 special-functions × 34 233 real-analysis × 50 111 polylogarithm × 24