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How to integrate (sec x)^4, help please

  1. Jan 2, 2006 #1
    May i know how to integrate (sec x)^4 ??

    the answer is tan x + 1/3 (tan x)^3
  2. jcsd
  3. Jan 2, 2006 #2


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    Try writing your integral as
    [tex] \int (\tan^{2} x + 1) \sec^{2} x dx [/tex]
  4. Jan 2, 2006 #3
  5. Jan 2, 2006 #4
    try using [tex]u=tg(x)[/tex]
    and [tex]\frac{1}{cos^2(x)}=1+tg^2(x)=1+u^2[/tex]
    Last edited: Jan 2, 2006
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