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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?

    Thanks,
    Casey
     
  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

    [tex]\int\sec^{2}{2x}\sec{2x}\tan{2x}dx[/tex]

    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
     
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