1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sec(x)tan(x) integral

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data
    [itex]∫sec(x)tan(x)+x/(x^2+1) dx[/itex]

    3. The attempt at a solution
    I replaced sec and tan by [itex]1/cos(x)[/itex] and [itex]sin/cos(x)[/itex] then end up with [itex]sin(x)/cos^2(x)[/itex]
    then I replace [itex]cos^2 x [/itex] by [itex]1-sin^2 x [/itex] then I dont know where to go.

    the second part of the equation works with u substitution.
    I just cant see where the identities of the first part are leading me.

    any hint? thanks in advance!
  2. jcsd
  3. Jan 27, 2014 #2


    User Avatar
    Homework Helper

    No, don't do that. Try the sub ##u = \cos x## and watch that sucker fold. :smile:
  4. Jan 29, 2014 #3
    you know i just used tan(x) in the first term and u substitution in the second and it worked too!

    Thanks a lot!
  5. Jan 29, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You should ideally recognize the derivative of sec x.
  6. Jan 30, 2014 #5


    User Avatar
    Gold Member

    For the first integral you don't have to substitute anything. It is the derivative of sec(x).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted