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Zaid Alyafeai

My book on advanced integration

http://advancedintegrals.com/advanced-integration-techniques.pdf

My Blog where I post some interesting integration problems and properties.

My Email: alyafey22[at]gmail[dot]com

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  • Member for 7 years, 7 months
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  • Last seen May 7 '20 at 18:53

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77 Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$ Aug 16 '13
44 Triple Euler sum result $\sum_{k\geq 1}\frac{H_k^{(2)}H_k }{k^2}=\zeta(2)\zeta(3)+\zeta(5)$ Dec 18 '13
32 Evaluating $\int^1_0 \frac{\log(1+x)\log(1-x) \log(x)}{x}\, \mathrm dx$ Aug 12 '13
27 Really advanced techniques of integration (definite or indefinite) Aug 7 '16
26 Calculating alternating Euler sums of odd powers Mar 3 '17
25 Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$ Aug 1 '13
21 A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$ May 22 '14
19 An integral of a rational function of logarithm and nonlinear arguments Apr 19 '17
19 Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$ Dec 25 '13
19 How can we show that $\int_{0}^{1}\cos(\ln x)\cdot{\mathrm dx\over 1+x^2}={\pi\over 4}\cdot{1\over \cosh\left({\pi\over 2}\right)}?$ May 10 '17
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