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!

More trig substitution help

  1. Jan 31, 2008 #1
    [SOLVED] More trig substitution help...

    I've looked at this problem about 3 times and still can't figure it out...where identity did they use to substitute out the part in the red box? Thanks for the help

  2. jcsd
  3. Jan 31, 2008 #2
    What's the step you don't understand?
    [tex] \int \tan^{4}x \mathrm{d}x = \int \tan^{2}x \left(\sec^{2}x - 1\right) \mathrm{d}x [/tex]
    [itex] \int \tan^{2}x \left(\sec^{2}x - 1\right) \mathrm{d}x = \int \tan^{2}x \sec^{2}x \mathrm{d}x - \int \tan^{2}x\mathrm{d}x[/itex].
  4. Feb 1, 2008 #3

    Gib Z

    User Avatar
    Homework Helper

    [tex]\sec^2 x - 1 = \tan^2 x[/tex] and [tex]\tan^2 x \cdot \tan^2 x = \tan^4 x[/tex].
  5. Feb 1, 2008 #4
    for me it's unclear how to integrate
    [tex]\int\tan^2 x\sec^2 x dx=\int (\sec^2 x-1)\sec^2 x dx=\int \frac{1}{\cos^4}dx-\tan x[/tex]
    So how to integrate
    [tex]\int \sec^4 dx[/tex]
  6. Feb 1, 2008 #5

    Gib Z

    User Avatar
    Homework Helper

    Integration by parts a few times does it, or write

    [tex]\int \sec^2 x (\tan^2 x + 1) dx [/tex] and let u= tan x.

    But rather than integrate sec^4, keep the original integral,
    [tex]\int \tan^2 x \sec^2 x dx = \int u^2 du[/tex] when u= tan x.
  7. Feb 1, 2008 #6
    I see
    [tex]\int\tan^2 x\sec^2 x dx=\int \tan^2 x d(\tan x)=\frac{1}{3}\tan^3 x+C[/tex]
    Last edited: Feb 1, 2008
  8. Feb 1, 2008 #7

    Gib Z

    User Avatar
    Homework Helper

    You forgot the x on the end of the tan, but other than that, its correct.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: More trig substitution help
  1. Trig substitution help (Replies: 6)

  2. Trig substitution help (Replies: 25)

  3. Trig substitution help (Replies: 6)