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 Apr18 reviewed Approve show a set is lebesgue measurable Apr18 awarded Custodian Apr18 answered Solid of revolution vs $\iiint$ Apr18 answered fourier series, parsevel's identity Apr17 awarded Organizer Apr17 revised Solving integral $\int \frac{x+\sqrt{1+x+x^2}}{1+x+\sqrt{1+x+x^2}}\:\mathrm{d}x$ It's really nothing to do with irrationals. Apr17 suggested approved edit on Solving integral $\int \frac{x+\sqrt{1+x+x^2}}{1+x+\sqrt{1+x+x^2}}\:\mathrm{d}x$ Apr17 comment Integral $I=\int_0^\infty \frac{x^4}{(\alpha+x^2)^4}dx$ @Integrals Substitute $t=u^2$, and use $$B(x,y)=\int_0^\infty \frac{t^{x-1}}{(1+t)^{x+y}}dx,$$ where $B(x,y)= \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}$ is the beta function. Apr17 awarded Talkative Apr17 comment How to convert a integral into the another? @Victor An excellent explanation is here. Apr17 comment Closed form for $\int_0^1 \frac{x^a dx}{(1+x^b)^c}$. This is essentially what the other answers do, the equivalence between their forms and your idea basically comes from the definition of the hypergeometric function. Apr17 comment Which $n$th order differential equations have $n$ linearly independent solutions? Thanks. However, you seem to have just proven the case for $n=2$, not general $n$ (or, indeed, for other types of differential equation). Apr17 comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$. @AlexB. I've encountered a few things that need $p$-adic numbers, but never a particularly good introduction on them. I know this is not really to do with the original question, but do you know of a good introduction? Regardless, thanks for the speedy response. Apr17 comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$. @AlexB. What theory is necessary to understand Tate's proof? Apr16 revised A question on convergence of Fourier series and the derivative of the function Fixed LaTeX Apr16 suggested approved edit on A question on convergence of Fourier series and the derivative of the function Apr16 revised Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$ added 504 characters in body Apr16 answered Integrate $\displaystyle \int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$ Apr16 comment Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$ @RandomVariable Oh, and only take the limit after differentiating? Apr16 comment Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$ @RandomVariable Is there a rigorous way one could justify that that would make the integral converge (I'm really bad with this, despite trying to learn some analysis)?