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## Homework Statement

I've got an equation which I need to integrate. However, integrating it and checking with the solutions, I get two different results. I get the same result as using wolfram alpha, but a different result from the book.

If I differentiate both results, I get back to the orginal equation, so I don't know why they are different.

## Homework Equations

Equation which I need to Integrate by seperation of variables: [tex]\frac{d\dot{x}^2}{dx} = \frac{2l^4 a^2 x}{(12x^2+l^2)^2}[/tex]

Result from Book: [tex]\dot{x}^2 = \frac{ l^2 a^2 x^2}{12x^2+l^2}[/tex]

Result from Wolfram-Alpha: [tex]\dot{x}^2 = -\frac{(a^2 l^4)}{(12 (l^2+12 x^2))}[/tex]

## The Attempt at a Solution

If I differentiate both, I'll both get the same equation back which I integrated, I just don't understand why thats the case, since it doesn't look like they differ by a additive constant.

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