Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Please Help with Trig Substitution Integration

  1. Feb 3, 2006 #1
    I am not too good with trig identities. I cant seem to figure out how to simplify these trig intergrals. I know I can use a triangle to turn the second problem into a trig integral, but once I have the trig integral, I am lost. Any help would be greatly appriciated.:redface:

    Last edited: Feb 3, 2006
  2. jcsd
  3. Feb 3, 2006 #2
    Have you tried a u-substitution on the first one yet? Here is a hint what is the derivative of sec?
  4. Feb 3, 2006 #3
    see, thats what I thought, but there seems to be an extra secant in there. The derivative of sec is sectan. So, u=sec(x), du=sec(x)tan(x)dx. That gives tan(x)sec^2(x)... right?
  5. Feb 3, 2006 #4


    User Avatar
    Science Advisor
    Homework Helper

    HINT: Let

    [tex]u = \cos x[/tex]

    It will save you a lot of work.
  6. Feb 3, 2006 #5
    [tex] u=sec(x) [/tex] [tex]du=sec(x) tan(x)dx [/tex]

    [tex] \int u^2du [/tex]
    Last edited: Feb 3, 2006
  7. Feb 3, 2006 #6
    brilliant! Thanks Tide. I should have seen that.
    [tex]\int\frac{sin(x)}{cos^4(x)}dx = \frac{1}{3cos^3(x)}[/tex]
  8. Feb 3, 2006 #7
    right, yes I can see that too Valhalla. Thanks so much. Looks like that one was much easier than I made it.
  9. Feb 3, 2006 #8
    Any ideas on the second problem? Using a triangle, I have changed it to:

  10. Feb 3, 2006 #9
    wait, I think got it, [tex]u=sin\Theta[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook