# Questions tagged [calculus]

For basic questions about limits, derivatives, integrals and applications, mainly of one-variable functions.

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### What can be said about the level set of the real part of an analytic function?

I am working with a function $F(z;a)$, for $z\in \mathbb{C}$ and $a$ being a set of parameters, from which I need to analyze the level set $\text{Re}(F(z))=0$ (for a fixed set of parameters $a$, which ...
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### Evaluating $\int_0^\pi \frac{x}{(\sin x)^{\sin (\cos x)}}\,\mathrm{d}x$

Evaluate $$\int_0^\pi \frac{x}{(\sin x)^{\sin (\cos x)}}\,\mathrm{d}x.$$ I tried using by parts and complex numbers along with series expansion but I was unable to find the answer. Please Help!
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### Question on the paper Donal F. Connon, “Some integrals involving the Stieltjes constants”

I'm reading Donal F. Connon, Some integrals involving the Stieltjes constants. It gives a definition of the generalized Stieltjes constants $\gamma_n(u)$ as coefficients in the Laurent series ...
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### The diferential equation $y' = \frac{\ln(x^2+y^2)}{x^2 + y^2}$

In my University, the integral calculus teacher gave me this diferential equation to solve. $$y' = \frac{\ln(x^2+y^2)}{x^2 + y^2}$$ I dont have any clue of what form has the solution of this ...
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### Juantheron-like integral

While seeing this post, the following integral is just struck me \begin{equation} \int_0^\infty \frac{dx}{(1+x^2)(1+\tan x)}\tag1 \end{equation} I have tried like what user @OlivierOloa did in his ...
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### Exact values of error function

The error function is defined as $$\operatorname{erf}(z)=\frac{2}{\sqrt{\pi}} \int_0^z e^{-t^2} \, dt.$$ We know that the Gaussian integral is $$\int_{-\infty}^{\infty} e^{-x^2}\,dx=\sqrt{\pi}.$$ ...
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