Let $f:\mathbb{R} \rightarrow \mathbb{R}$ such that
\begin{equation} f(x)+f\left(1-\frac1x\right)=\arctan x \quad \text{forall} \; x \neq 0\end{equation}
(As usual $y = \arctan x $ means $-\pi/2<y<\pi/2$ and $\tan x = y$.)
Evaluate the integral $\displaystyle \int_0^1 f(x) \, {\rm d}x$.
Putnam 2016 A3
Putnam 2016 A3
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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