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 xZ tan 2 x sec x dx = sec x tan xZ (sec 2 x1) sec x dx = sec x tan xZ sec 3 x dx + Z sec x dx....
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 Fall '07
 JonathanRogawski
 Math, Calculus, Integration By Parts, dx, 3 Sec

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