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12h
comment Evaluate $\int\left({\frac{\arctan x}{\arctan x-x}}\right)^2 \,dx$
math.stackexchange.com/questions/79074/…
21h
comment Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$
Very nice answer. +1 After about 30 minutes of getting nowhere, I gave up.
21h
revised Prove this polylogarithmic integral has the stated closed form value
edited body
22h
revised Prove this polylogarithmic integral has the stated closed form value
corrected typos
1d
answered Prove this polylogarithmic integral has the stated closed form value
1d
revised Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
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1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
@robjohn Isn't the difference that you shifted the contour while I moved the pole?
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
@robjohn Not long after I posted this question earlier this year, I realized why my original approach was wrong. So I modified my approach and explained what I did in the original post. Another user bumped this thread today, and when I looked at my post, I realized it could be made a lot clearer. So I edited it. If you have another way to evaluate it using contour integration, please post it. EDIT: I see you already have. :)
1d
revised Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
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2d
revised Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
deleted 1 character in body
2d
revised Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
added 12 characters in body
2d
answered Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
Jul
23
revised About a harmonic series problem : How to prove that $\sum_{n=1}^{\infty}\frac{H_n}{n^3}=\frac{\pi^4}{72}$
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Jul
23
comment About a harmonic series problem : How to prove that $\sum_{n=1}^{\infty}\frac{H_n}{n^3}=\frac{\pi^4}{72}$
Nice answer. +1 I also liked your evaluation of that bino-harmonic sum. math.stackexchange.com/questions/815103/… Your approach to that sum simplified the evaluation considerably.
Jul
23
awarded  Good Answer
Jul
23
revised $\int_0^\infty\text{Ci}(x)^3\mathrm dx$
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Jul
22
revised $\int_0^\infty\text{Ci}(x)^3\mathrm dx$
edited tags
Jul
22
answered $\int_0^\infty\text{Ci}(x)^3\mathrm dx$
Jul
20
awarded  Popular Question
Jul
20
answered Which contour is best for $\int_0^\infty\frac{1}{x^2 + x + 1}dx$