Results 1 to 3 of 3

Math Help - tan reduction formula

  1. #1
    Junior Member Tclack's Avatar
    Joined
    Oct 2009
    From
    No permanant location.
    Posts
    57
    Thanks
    1

    tan reduction formula

    So the proof for the reduction formula for [tan(x)]^n I found here, and it makes sense

    But I did this and it is very close, but not the same formula, what's wrong?

     \int tan^nx dx = \int tan^n^-^2x *tan^2x dx
     =\int tan^n^-^2x(sec^2x -1) dx
    = \int tan^n^-^2x*sec^2x dx - \int tan^n^-^2x dx

    here I did an integration by parts of the first integral above:

     u= tan^n^-^2x,,,,,,,,,,,,,,,dv=sec^2xdx
    du=(n-2)tan^n^-^3xdx,,,,,,v=tanx

     uv-\int vdu

     tan^n^-^1x-(n-2)\int tan^n^-^2xdx - \int tan^n^-^2xdx

    so I get
     \int tan^nx = tan^n^-^1x-(n-1)\int tan^n^-^2xdx Where's did I go wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    The derivative of \tan^{n-2} x is not (n-2) \tan^{n-3} x. Do you see why?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Tclack's Avatar
    Joined
    Oct 2009
    From
    No permanant location.
    Posts
    57
    Thanks
    1

    Wink Oh yeah!

    Yeah, the Chain Rule. Thanks for the backup
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using a Reduction Formula
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 7th 2009, 12:43 PM
  2. Reduction formula
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 26th 2009, 02:26 AM
  3. need help with reduction formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 24th 2009, 09:01 PM
  4. Reduction Formula
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 26th 2008, 09:35 AM
  5. Reduction Formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2008, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum