Inspired by Rishabh Cool

Calculus Level 3

\[ -\dfrac12 \ln\left( \dfrac{1-x}{1+x} \right) \qquad \qquad \text{arctanh} x \qquad \qquad \dfrac12 \ln \left( \dfrac{1+x}{1-x} \right) \]

Consider a function \(f(x) \) whose series is \( \displaystyle \sum_{n=1}^\infty \dfrac{x^{2n-1}}{2n-1} \), where \(|x| < 1\). How many of the 3 functions above is/are a closed form of \(f(x) \) for \(|x| < 1\)?


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