How to use inverse hyperbolic functions to evaluate integrals

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Sometimes you're going to run into an integral that seems impossible to solve. U-substitution doesn't work, integration by parts doesn't work, it's not a partial fractions problem, and the other techniques you try leave you nowhere. Or sometimes you'll know how to simplify the integral using one of these techniques, but, even though you've made the function simpler, you can't integrate what you have left. What do you do?

Well, not always, but sometimes you'll need to use an inverse hyperbolic function to take the integral. If you're able to memorize these integration formulas, they can come in really handy and save you a ton of time and frustration.

What you'll want to do is determine whether or not the function you have left to integrate matches exactly one of these integration formulas, and then apply the formula. Your messy integral, the one you can't evaluate, will magically turn into an inverse hyperbolic function, right before your eyes. In this video, we do an example where the integral of the function turns into hyperbolic sine.

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Видео How to use inverse hyperbolic functions to evaluate integrals канала Krista King