Textbook Problem

Comparing Methods Find the indefinite integral

${\displaystyle \int \sec x\cos xdx}$

using the given method. Explain how your answers differ for each method.

(a) Substitution when $u=\sin x$

(b) Substitution where $u=\cos x$

(c) Integration by parts

(d) Using the identity $\sin 2x=2\sin x\cos x$