Indefinite Integral: $\int \frac{1}{\sqrt{\sin 2x}}dx$

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SUMMARY

The integral $\int \frac{1}{\sqrt{\sin 2x}}dx$ is classified as an elliptic integral of the first kind, indicating that it cannot be expressed in terms of elementary functions. Participants in the discussion confirmed that standard techniques for integration do not apply, and the solution involves advanced methods typically used in elliptic integrals. The discussion emphasized the importance of recognizing the nature of such integrals for proper evaluation.

PREREQUISITES
  • Understanding of elliptic integrals and their classifications
  • Familiarity with integral calculus and advanced integration techniques
  • Knowledge of trigonometric identities, specifically related to $\sin 2x$
  • Experience with mathematical notation and expressions in calculus
NEXT STEPS
  • Study the properties and applications of elliptic integrals of the first kind
  • Learn techniques for evaluating non-elementary integrals
  • Explore trigonometric identities and their role in integration
  • Investigate numerical methods for approximating elliptic integrals
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Mathematicians, calculus students, and anyone interested in advanced integration techniques and the study of elliptic integrals.

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$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$
 
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jacks said:
$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$

How are you expecting this to be expressed? It is not elementary, but is an elliptic integral of the first kind.

CB
 
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