1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Integral Help

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    solve the integral.

    2. Relevant equations
    integral (sec(x)^2 / 4+tan(x)^2)

    3. The attempt at a solution
    i tried replacing the numerator with the trig identity: tan(x)^2 + 1 -- but not sure what else to try.
  2. jcsd
  3. Feb 16, 2013 #2
    There is a very obvious substitution you can do here.
  4. Feb 16, 2013 #3
    Consider the derivatives of trigonometric functions.
  5. Feb 16, 2013 #4
    was the step i performed correct?
  6. Feb 16, 2013 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member


    What is the derivative of tan(x) ?
  7. Feb 16, 2013 #6
    What is d/dx (tanx)?
    Edit: or what sammy says :)
  8. Feb 16, 2013 #7
    Also, be careful that an integral is not the same thing as an antiderivative.
  9. Feb 16, 2013 #8


    User Avatar
    Science Advisor

    The first thing I would do is replace sec2(x) with 1/cos2(x) and replace tan2(x) with sin2(x)/cos2(x).
  10. Feb 16, 2013 #9

    I wouldn't do this, but I would take a look at tanx and what the derivative is, it does become pretty hard though and you need a trig substitution afterwards, I think I did this exact problem before.
  11. Feb 17, 2013 #10
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook