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: Integrating cos^-2(x) after inverse substitution

  1. Feb 13, 2008 #1
    1. The problem statement, all variables and given/known data

    Use the substitution x=4sin(t) to evaluate the integral: S 1/[(16-x^2)^(3/2)] dx

    2. Relevant equations

    x = 4sin(t)

    3. The attempt at a solution

    x = 4sin(t)
    dx = 4cos(t) dt

    4cos(t) = (16-x^2)^(1/2), i cube both sides to get

    (4cos(t))^3 = (16-x^2)^(3/2), then plug in dx and denominator into the equation to get

    S 4cos(t)/[(4cos(t))^3] dt simplified and constant taken out i now get
    (1/16) S [cos^-2(t)] dt

    how do i integrate cos^-2(t) to get a simple answer. I don't think i can use the S cos^n(t) formula because then i have to integrate sin^-4(t) afterwards.

    any help would be awesome, thanks
  2. jcsd
  3. Feb 13, 2008 #2


    User Avatar

    cos^-2(x) = sec^2(x)

    Integral of sec^2(x) = tan(x)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook