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: Help trig integral question

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral

    integral of (tanx)^5*(secx)^4

    2. Relevant equations

    3. The attempt at a solution

    what I did was broke the sec^4x into 2 sec^2's multiplied by each other
    then one of these terms became tan^2x +1
    so I had tan^5x*(tan^2x + 1)*sec^2x

    then u = tanx
    du = sec^2x

    eventual answer tan^8x/8 + tan^6x/6 + c

    however the book shows this problem by taking a (secxtanx) out of eveyrthing then doing tan^4x = (sec^2x -1)^2*sec^3x
    u= secx
    du = tanxsecx

    eventual answer sec^8x/8 - sec^6x/3 + sec^4x/4 + C

    ...is there something wrong with the way I did it; I don't see anything wrong with the way I'm doing it but the book insists on doing all problems like this the otherway. I wouldn't mind but I don't like memorizing things and the way I always seem to think of doing these problems is the first method I wrote out please respond I have an exam on this stuff tomarrow night
  2. jcsd
  3. Feb 26, 2008 #2

    [tex]\int\sec^{3}x\tan^{4}x(\sec x\tan x)dx[/tex]

    [tex]\int\sec^{3}x(\sec^{2}x-1)^2(\sec x\tan x)dx[/tex]
  4. Feb 26, 2008 #3
    yes that is how the book does it but why is the way that I did it wrong I don't get it?
  5. Feb 26, 2008 #4
    Your way ...



    I guess just have confidence in yourself. You did it all the steps correctly, but through a different route.
    Last edited: Feb 26, 2008
  6. Feb 26, 2008 #5
    ok thanks alot; and wow thats a good way to proove it I didn't think of that
  7. Feb 26, 2008 #6
    I take that back. I tried it and it didn't work, lol. But your solution is still right, but the limits of Integration is a different story.
  8. Feb 27, 2008 #7
    ah yea that does make sense that you would need different limits
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook