Integrating Inverses of FunctionsAnother way to integrate

Chapter 8, Problem 75E

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Problem 75E

Integrating Inverses of Functions

Another way to integrate f-1(x) (when f-1 is integrable, of course) is to use integration by parts with u = f-1(x) and dv = dx to rewrite the integral of f-1 as

Equations (4) and (5) give different formulas for the integral of cos-1 x:

Can both integrations be correct? Explain.

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