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Homework Help: Stuck on a calc problem

  1. Mar 17, 2005 #1
    I need to get the integral for sqrt(25+x^2). I can't seem to get the answer without a arcsinh. Can anyone help me? Thx in advance! :)
  2. jcsd
  3. Mar 17, 2005 #2
    Substitute [tex] x = 5\tan{\theta}[/tex].

    You may need the identity [tex] \int \sec{\theta} d\theta = \ln |\sec{\theta} + \tan{\theta}| + C[/tex] to evaluate the resulting integral.
    Last edited: Mar 17, 2005
  4. Mar 17, 2005 #3


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    Science Advisor

    Generally speaking, seeing "sqrt(25+ x2)" should make you think of
    a2+ b2= c2 (the Pythagorean theorem) and then
    (a/b)2+ 1= (c/a)2 or "tan2(θ)+ 1= csc2(θ)"

    Factoring a "5" out of the squareroot gives 5 sqrt(1+ (x/5)2) which leads us to think "x/5= tan(θ) or Data's x= 5 tan(θ).
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