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: Antiderivative of Secant

  1. Sep 19, 2006 #1
    For one of my homework assignments, I had to find the integral of a function. I got my function simplified to sec(t)^(8/3). I tried to use the reduction formula for sec(t)^n, but I believe that it only works if the power of sec is an integer. Could somebody help me out, please?

    Edit: I figured that it might be a good idea if I showed how I got to sec(t)^(8/3)

    My initial problem was the following: integral of cube root(1+x^2) dx.

    First of all, I made the substitution x=tan(t) and dx = sec(t)^2 dt. This gave me:

    integral of cube root(1+tan(t)^2) * sec(t)^2 dt.

    I changed 1+tan(t)^2 to sec^2 to get the following:

    integral of sec(t)^(2/3) * sec(t)^2 dt, or sec(t)^8/3.

    Did I take this problem in the wrong direction, or am I on the right track?
    Last edited: Sep 19, 2006
  2. jcsd
  3. Sep 19, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It probably doesn't have an elementary antiderivative. Mathematica expresses it in terms of a hypergeometric function.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook