Chapter 5.5, Problem 91E

Looking ahead: Integrals of sec x and csc x

1. a. Multiply the numerator and denominator of sec x by sec x + tan x; then use a change of variables to show that

${\displaystyle \int \sec xdx=\ln |\sec x+\tan x|+C.}$

1. b. Use a change of variables to show that

${\displaystyle \int \csc xdx=-\ln |\csc x+\cot x|+C.}$