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Trig Integration By Substitution

  1. Sep 15, 2014 #1
    Mod note: Moved from technical math section
    ∫(2x+6)/sqrt(5-4x-x^2)

    I have 2/3(ln|tan(theta)+sec(theta)|-3|cos(theta)|) where x=sin^-1((x+2)/3)
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Sep 15, 2014 #2

    SteamKing

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    Are there supposed to be two x^2 expressions under the SQRT?
     
  4. Sep 15, 2014 #3
    Apologies no it should be 5-4x-x^2
     
  5. Sep 25, 2014 #4

    HallsofIvy

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    Complete the square in the square root: [tex]5- 4x- x^2= 5- (x^2+ 4x+ 4- 4)= 5- (x+ 2)^2+ 4= 9- (x+ 2)^2.

    Now make the substitution u= x+ 2, du= dx, x= u- 2 so 2x+ 6= 2u+ 2. The integral becomes [tex]\int \frac{2u+ 2}{\sqrt{9- u^2} du[/tex]

    Now let [itex]u= 3 sin(\theta)[/itex].
     
  6. Sep 25, 2014 #5

    Mark44

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    Homework-type problems should be posted in the Homework & Coursework section. I have moved this thread.
     
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