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Integral homework help

  • Thread starter Ed Aboud
  • Start date
197
0
1. Homework Statement

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

2. Homework 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.
 

Dick

Science Advisor
Homework Helper
26,258
618
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).
 
197
0
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!
 

Dick

Science Advisor
Homework Helper
26,258
618
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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