Integral trouble trig

  • Thread starter Jbreezy
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  • #1
Jbreezy
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Homework Statement



Integral of dt/ (√(t^2 -6t + 13)

Homework Equations


I sub
v = t-3, and v = 2tan(θ)




The Attempt at a Solution



first I completed the square of t^2 -6t + 13, I got (t-3)^2 +4

Also I say v = t-3
∫ dv/ (√(v^2 +4)
I then sub in trig

∫(2sec^2(θ)dθ / 2√(tan^2(θ) +1) = ∫ (sec^2(θ)/ secθ)dθ

= ln|secθ +tanθ| = ln|(√v^2+4)/2 + v/2| edit sec here
= ln| √((t-3)^2 +4/2) + (t-3)/2| +c
I feel it isn't correct. What did I do?
 
Last edited:

Answers and Replies

  • #2
vela
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One thing you did was write ##\sec\theta## in terms of ##v## incorrectly.
 
  • #3
Jbreezy
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OK, I fixed it. I flipped it back it was OK on my paper just not when I rewrote it on the forum.
 
  • #4
vela
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Try differentiating your result and seeing if you recover the integrand. That's the easiest way to check your answer.
 

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