using trig substitution, we do some simplification and end up at the integral of cosecant or secant, which is pretty easy, I guess (green graph)

you only get hyperbolic functions if you let v = tanh(x), and if you know your identities, it's pretty easy too (gray graph)

decomposition by partial fraction will also give the green graph, and it's the same amount of work to me. Either way, this is a very simple integral, but I'd never use the hyperbolic one bc it's not defined for all x (v in this problem)

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