Inverse hyperbolic functions follow standard rules for integration. Remember, an inverse hyperbolic function can be written two ways. For example, inverse hyperbolic sine can be written as arcsinh or as sinh^(-1). Some people argue that the arcsinh form should be used because sinh^(-1) can be misinterpreted as 1/sinh. Whichever form you prefer, you see both, so you should be able to recognize both and understand that they mean the same thing.
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