Another way to integrate -1 (x) (when -1 is integrable, of course) is to use

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

compare the results of using Equations (4) and (5).

Equations (4) and (5) lead to different formulas for the integral of tan^-1 x:

a.

b.

Can both integrations be correct? Explain.

Transcribed Image Text:

√5-100 [1-¹0x) dx ƒ-¹(x) dx = xf-¹(x) - [x ( a + 1-1(x) dx. dx (5)