David H
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 62 Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$ 33 Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$ 24 Why do some mathematical ideas seem counter-intuitive? 19 A closed form for a lot of integrals on the logarithm 18 Interesting and unexpected applications of $\pi$

### Reputation (18,328)

 +5 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 +10 Why do some mathematical ideas seem counter-intuitive? +10 CAS Can't Solve the Integral +10 Need help with $\int_0^1 \frac{\ln(1+x^2)}{1+x} dx$

### Questions (26)

 22 Definite integral of arcsine over square-root of quadratic 21 Integrals of integer powers of dilogarithm function 20 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 13 Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}$ 12 How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?

### Tags (158)

 684 integration × 215 176 sequences-and-series × 52 617 calculus × 177 141 hypergeometric-function × 16 495 definite-integrals × 128 118 improper-integrals × 32 186 closed-form × 36 98 polylogarithm × 22 182 real-analysis × 45 84 trigonometry × 42

### Accounts (24)

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