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Calculus Problem Help Integral of (secx)^3 dx

  1. Oct 4, 2004 #1
    Hi all, I am stuck on this trig integral problem. The answer is provided in the book, but I do not know how to get it. The problem is this:

    Integral of (secX)^3 dx

    it says first use integration by parts:

    u = sec x du = sec x tan x dx

    dv = (secx)^2 dx v = tan x

    uv - integral (v du) = sex x tan x - integral sec x((secx)^2-1) dx

    Then it says secx tanx - integral (sec x)^3 dx + integral sec x dx

    Now there is another (sec x)^3 like in the original problem, after this step they just provide the answer, but how ?

    The answer is 1/2(secxtanx + ln |secx+tanx|) + C
  2. jcsd
  3. Oct 4, 2004 #2


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    Hence, you have shown:
    Can you take it from there?
  4. Oct 4, 2004 #3
    hmm, let me try, thats diff. method from the book but it looks easier, brb. thx.
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