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How to change ∅ in term of x? (integration by trigonometry substitution)

  1. Oct 5, 2012 #1
    the question is ∫dx/ x^2*√(x^2-1)

    I use x=a sec ∅ x^2*√(x^2-1)= sec^2∅tan∅ x=sec ∅
    dx= sec∅tan∅d∅

    so it will become something like this ∫sec∅tan∅d∅/sec^2∅tan∅= ∫1/sec∅d∅=∫cos∅d∅
    =sin∅+c
    But how can i change this sin in term of x?
     
  2. jcsd
  3. Oct 5, 2012 #2
    You said [itex]x = a \sec \theta[/itex].

    Can you draw a right triangle for which this is true and solve for the lengths of each of the sides?
     
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