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 Jul 25 awarded Nice Answer Jul 16 comment Inequality Related to $\arctan$ function @Fabian except $x = 0$ ;) Jul 16 comment How do I calculate the limit of this integral? Your question is related to this one: math.stackexchange.com/questions/160248/… Jul 15 comment Sum equals integral Actually I would be more interested in neat examples rather than general methods for finding such functions. Jul 14 comment Sum equals integral @RossMillikan If summation of a series would range also from $-\infty$ to $+\infty$ than ${\rm sinc}$ is a nice example. Jul 14 asked Sum equals integral Jul 9 comment Find the functions family that satisfies the inequality $\int_0^1 \frac{dx}{1+f^{2}(x)} <\frac{f(1)}{f'{(1)}}$ @Mercy it is derivative which is not increasing. Jul 9 comment Find the functions family that satisfies the inequality $\int_0^1 \frac{dx}{1+f^{2}(x)} <\frac{f(1)}{f'{(1)}}$ Here's my first though: If we assume that: $f'$ is continuous and not increasing; $f'(1) \neq 0$; $f(0) = 0$; $f(1) \ge 0$, than: $$\int_0^1 \frac{f'(x)}{1 + f^2 (x)} \cdot \frac{dx}{f'(x)} \le \frac{\arctan f(1)}{f'(1)} \le \frac{f(1)}{f'(1)}$$ Jun 29 revised Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx$ Fixed formula look Jun 29 suggested approved edit on Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx$ Jun 28 answered Solving a complex integral Jun 26 comment gradient in polar coordinate by changing gradient in Cartesian coordinate You wrote: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x}$$ instead of: $$\frac{\partial \phi}{\partial x} = \frac{\partial \phi}{\partial r} \frac{\partial r}{\partial x} + \frac{\partial \phi}{\partial \theta} \frac{\partial \theta}{\partial x}$$ Jun 26 answered Visualizing Commutator of Two Vector Fields Jun 26 answered Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$? Jun 26 comment Two sums for $\pi$ @daniel I missed the link :( Ok, I'll try to make it more complete and then I'll post it there. Jun 26 answered Two sums for $\pi$ Jun 25 comment A linear differential equation @rubik ok, here it goes. Jun 25 answered A linear differential equation Jun 24 revised Series Expansion added 143 characters in body Jun 24 answered Series Expansion