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## Homework Statement

You know the U substitution proofs for inverse trig functions that go like this:

[itex]\int\frac{1}{a^{2}+x^{2}}dx[/itex]

[itex]\int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx[/itex]

let u = x/a

du= dx/a

....

[itex]\frac{1}{a}tan^{-1}(x/a)+c[/itex]

I have searched google and can't find any of these proofs for the other trigonometric functions like sin and tan. Where can I find step by steps of these particular integration generalizations?

Do these U substitution methods for inverse trig functions have some sort of specific name?