- #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.

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- Thread starter Ed Aboud
- Start date

- #1

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

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

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

Thanks.

- #2

Dick

Science Advisor

Homework Helper

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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

Science Advisor

Homework Helper

- 26,263

- 619

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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