Integral homework help

  • Thread starter Ed Aboud
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  • #1
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Homework Statement



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

Homework Equations





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.
 

Answers and Replies

  • #2
Dick
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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).
 
  • #3
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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!
 
  • #4
Dick
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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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