Mathematics

Problem

For

x>1

, let

I = \int \sec^{-1} x\, dx

. a. (i) Show that

I = x\sec^{-1}x - \ln\left|x + \sqrt{x^{2}-1}\right| + C

, where

C

is the constant of integration. b. (ii) Verify your result in part (i) by differentiating the right–hand side and simplifying.