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Homework Help: Integral from 0 to 1 of 1/sqrt(1+x^2)

  1. Jan 17, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int_0^1 \frac{1}{\sqrt{x^2+1}}\,dx[/tex]

    2. Relevant equations
    Integration by substitution looks like it might help here...

    3. The attempt at a solution
    The answer is [tex]\log (1+\sqrt 2)[/tex], but I'm at a loss as to how to derive that.
  2. jcsd
  3. Jan 17, 2009 #2


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    Homework Helper

    You could try a trig substitution such as [itex]x=tan\theta[/itex].Hyperbolic trig sub. would be possible as well.
  4. Jan 17, 2009 #3
    Thanks. I worked it out using your suggestion, but x = sinh(theta) also works, in case anyone cares. :-)
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