Integral involving a square root which I can't work out

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SUMMARY

The integral ∫ y / (√(a(y^2)-c)) dy can be solved by recognizing that the integrand can be expressed as the derivative of a function involving a square root. Specifically, rewriting the integrand in the form of √(a(y^2)-c) allows for the application of integration techniques involving substitution. This approach simplifies the integral and leads to a solvable form. The constants 'a' and 'c' play a crucial role in determining the specific method of integration.

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  • Understanding of integral calculus and techniques of integration
  • Familiarity with substitution methods in integration
  • Knowledge of derivatives and their relationship to integrals
  • Basic algebraic manipulation skills
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  • Research integration techniques involving square roots, specifically focusing on substitution methods
  • Study the properties of definite and indefinite integrals
  • Explore advanced integration techniques such as integration by parts
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Homework Statement



Hi, I'm stuck on the following integral.

∫ y / (√(a(y^2)-c)) dy

where a and c are constants

Homework Equations



The Attempt at a Solution



I've tried using standard integrals involving square roots in the denominator, but I'm unsure what to do with the y on the numerator.

Any help would be appreciated!
 
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Hint: Write the integrand as the derivative of a function of the form √(______).
 

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