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: U Substitution 1

  1. Sep 12, 2007 #1
    So I have another U substitution.

    [tex]\int sec^3(2x)tan(2x)[/tex] this one is a little tricky for me. I have tried letting u= sec2x and tanx and 2x.
    2x definitley gets me nowhere. I may be mistaken on the others. I will recheck them.

    I was also thinking of rewriting it as
    [tex]\int sec^4(2x)sin(2x)[/tex]

    is the latter the better option?

  2. jcsd
  3. Sep 12, 2007 #2
    Unless I am mistaken, u = sec2x should work.
  4. Sep 12, 2007 #3
    Oh...one second, let me re-work this.
  5. Sep 12, 2007 #4
    I must be missing something...

    [tex]\int sec^32xtan2x[/tex] If u=sec2x du=2sec2xtan2x dx
    [tex]\rightarrow \int u^3 tan2x[/tex]

    wait....how about

    [tex]\int sec2xtanx*u^2 dx[/tex]
    =[tex]\frac{1}{2}\int u^2du[/tex]

    Thanks...Btw, how do you make a new line with Latex? I though it was \\
    Last edited: Sep 12, 2007
  6. Sep 12, 2007 #5
    your last 2 lines look funny to me, from what i have written down it should look like


    subst. [tex]\sec{2x}tan{2x}dx[/tex] with [tex]du[/tex]

    [tex]\frac{1}{2} \int u^{2}du[/tex]

    your final integral looked good but the one b4 doesn't click with me. i also thought \\ starts a new line, it works sometimes, and others it doesn't. the \ doesn't even work great for me either.
  7. Sep 12, 2007 #6
    I edited to fix..I forgot the tan2x where sec2xtan2x=du/2
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook