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Integral homework help

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm trying to solve [tex] \int \frac{dy}{\sqrt{y^2 + C}} [/tex]

    2. Relevant equations



    3. The attempt at a solution

    Is it [tex] ln |y + \sqrt{y^2 + C^2} | [/tex]

    Or is it [tex] sinh^-^1 [/tex] something.

    Thanks.
     
  2. jcsd
  3. Nov 25, 2008 #2

    Dick

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    Re: Integral

    It might be both, your first expression looks rather like sinh^(-1) to me as well. Why don't you try doing it? Put y=C*sinh(u) (assuming you mean y^2+C^2 in the integrand).
     
  4. Nov 25, 2008 #3
    Re: Integral

    It turns out that its [tex] sinh^-^1 (\frac{y}{c}) [/tex]

    Because my original differential equation was [tex] \frac{d^2y}{dt^2} - y = 0 [/tex]

    Thanks!
     
  5. Nov 25, 2008 #4

    Dick

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    Re: Integral

    arcsinh(y/C)=ln(y/C+sqrt(y^2/C^2+1)). That's the same as ln(y+sqrt(y^2+C^2)) up to a constant. They are both right.
     
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