This is about several ways how to integrate the hyperbola function (not using the chain rule). Some ways may be not so common. This article is not about new mathematical results, but focusses on several ways while always keeping in mind the students' perspective. From a purely mathematical point of view, the article could be read as proposing several alternatives on how to define $\exp(x)$ or $\ln(x)$, but this would not be the author's intention. He argues from the students' view, so this article is about several alternatives on how to obtain the area under the hyperbola function. At the end, the relation of $\ln 2$ to the harmonic series will be discussed.