**Unformatted text preview: **x dx =-x cos x + sin x + C. EXAMPLE 8.13 Evaluate Z sec 3 x dx . Of course we already know the answer to this, but we needed to be clever to discover it. Here we’ll use the new technique to discover the antiderivative. Let u = sec x and dv = sec 2 x dx . Then du = sec x tan x and v = tan x and Z sec 3 x dx = sec x tan x-Z tan 2 x sec x dx = sec x tan x-Z (sec 2 x-1) sec x dx = sec x tan x-Z sec 3 x dx + Z sec x dx....

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- Fall '07
- JonathanRogawski
- Math, Calculus, Integration By Parts, dx, 3 Sec