Page 28 - Calculus for the Clueless, Calc II

2
m and n are odd; u = sec x; du = tan x sec x dx. Break off one tan and one sec. Write each remaining tan x as
2
sec x - 1.

Example 8—

where m and n are even. This is one of my favorites. If m and n are even, and, in this problem, even though
2
2
there is no tangent, we let u = tan x, du = sec x dx, break off two of the secants, and write the remaining sec x
2
as tan x + 1.

Example 9—

where m (power of tan) is odd and n (power of sec) is even. We can let u = tan x or v = sec x. We will do it both
ways. Neither is too bad.

Example 9A—

Example 9B—