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visits member for 1 year, 7 months
seen 30 mins ago

4h
comment $\int_0^1 [ \frac{1}{x(x-1)} (2\mathrm{Li}_2(\frac{1-\sqrt{1-x}}{2})-\log(\frac{1+\sqrt{1-x}}{2})^2 ) -\frac{\zeta(2)-2\log^2 2}{x-1} ]dx$
@Integrals The main question involves two equalities. Are you unsure about how to prove both or only the last?
4h
reviewed Approve suggested edit on Good Textbooks for Real Analysis and Topology.
4h
reviewed Approve suggested edit on Normal distribution and option pricing
7h
comment About a harmonic series problem : How to prove that $\sum_{n=1}^{\infty}\frac{H_n}{n^3}=\frac{\pi^4}{72}$
The final link is dead now.
8h
comment Compute $\int_0^\infty \frac{\ln x}{(1+x)^3}\,\mathrm{d}x$
Do you know differentiating under the integral?
9h
reviewed Approve suggested edit on A fascinating number chain.
9h
reviewed Approve suggested edit on A problem on mathematical induction
2d
reviewed Approve suggested edit on Does a solution to the differential equation $y'=y$ exist?
2d
reviewed Approve suggested edit on show a set is lebesgue measurable
2d
awarded  Custodian
2d
reviewed Approve suggested edit on poincare-bendixson theorem contradiction
2d
answered Solid of revolution vs $\iiint$
2d
comment How to find $\nabla$ in spherical coordinates
I'd have thought that $x=r\sin \theta \cos\phi, y= r \sin \theta \sin \phi, z=r \cos \theta$ and the chain rule for partial derivatives is enough (though messy).
2d
answered fourier series, parsevel's identity
Apr
17
awarded  Organizer
Apr
17
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.
Apr
17
suggested suggested edit on Solving integral $ \int \frac{x+\sqrt{1+x+x^2}}{1+x+\sqrt{1+x+x^2}}\:\mathrm{d}x $
Apr
17
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.
Apr
17
awarded  Talkative
Apr
17
comment How to convert a integral into the another?
@Victor An excellent explanation is here.