David H
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 51 Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$ 28 Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$ 23 Why do some mathematical ideas seem counter-intuitive? 19 A closed form for a lot of integrals on the logarithm 17 Interesting and unexpected applications of $\pi$

### Reputation (14,659)

 +10 Express $C_n = \cosh(0) + \cosh(1) + \cosh (2) + \dots + \cosh(n)$ +10 Find the closed form of the digamma related series +35 What is a $0\times0$ or $0\times3$ matrix? +10 Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$

### Questions (18)

 19 Integrals of integer powers of dilogarithm function 17 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 11 Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}$ 10 How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$? 9 Evaluation of a dilogarithmic integral

### Tags (153)

 454 integration × 177 120 closed-form × 22 449 calculus × 151 106 hypergeometric-function × 10 324 definite-integrals × 94 94 improper-integrals × 29 150 sequences-and-series × 51 73 trigonometry × 41 144 real-analysis × 38 59 multivariable-calculus × 49

### Accounts (23)

 Mathematics 14,659 rep 21954 Physics 1,229 rep 415 Philosophy 610 rep 312 Astronomy 382 rep 111 History 221 rep 17