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Need alternate solution to a problem please help

  1. Aug 10, 2008 #1
    Hi, I posted a thread earlier with

    int/ 1/(1-x^2)^3

    I was able to solve it w/ partial fractions but it took 4 pages...
    Can you do this problem w/o partial fractions

    Please help :(
  2. jcsd
  3. Aug 10, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    No, partial fractions is the right way to do it.
  4. Aug 10, 2008 #3
    Try using substitution
    x = sin t ?

    I got int {1/cos^2 t}.dt
    There might be a shortcut to solve this in one line ...
  5. Aug 10, 2008 #4
    I get that there would be a cos upstairs and a cos^6 downstairs so it becomes 1/Cos^5, or sec^5. Not sure if that would be any easier than partial fractions.
  6. Aug 10, 2008 #5
    let's see:
    =1/(1-x^2)^3 .dx

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

    =cos/(1-sin^2)^3 .dt

    =1/cos^5 dt

    Yes, you are right, I forgot (^3).

    It seems messier

    >> syms x;
    >> f = sec(x)^5

    f =


    >> int(f,x)

    ans =

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