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Homework Help: What is the indefinate integral

  1. Sep 7, 2005 #1
    :confused: :confused: i have this question can any one help me plz thx.


    what is the indefinate integral of tan^7xsec^4x goodluck.
     
  2. jcsd
  3. Sep 7, 2005 #2

    TD

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    What have you tried so far?
     
  4. Sep 7, 2005 #3
    :redface:
    i am not yet to that grade lvl yet so that is why i want some one to post this explaing how to do it and little back ground to this thx :biggrin:
    :surprised
     
  5. Sep 7, 2005 #4
    Basically, I believe you must simply save a factor of [tex] \sec ^ 2 x[/tex]

    and use [tex]\sec ^ 2 x = 1 + \tan ^ 2 x [/tex] to express the remaining factors

    in terms of [itex] \tan x [/itex]. Next, simply substitute with respect to [tex] \tan x [/tex].

    (I think it's called "u"-substitution in some texts).?


    As you should already know, :shy:
    [tex] \frac{d}{dx} \tan x = \sec ^ 2 x [/tex]

    *Here's that method, put in action :smile: :
    [tex] \int {\tan ^7 x\sec ^4 x\,dx} = \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\sec ^2 x\,dx} = [/tex]
    [tex] \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\,d\left( {\tan x} \right)} = \boxed{\frac{{\tan ^8 x}}{8} + \frac{{\tan ^{10} x}}{{10}} + C} [/tex]

    !It is very likely that somewhere I made an error!....:frown: :frown: :frown:
    Somewhere...some silly error :rolleyes:
     
    Last edited: Sep 7, 2005
  6. Sep 7, 2005 #5
    thx a lot.
     
  7. Sep 8, 2005 #6

    TD

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    No, this is correct :smile:
     
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