Here are the top 30 Integral and Trigonometric Identities, along with the latex syntax and any explanatory text for each identity:

Trigonometric Relationships

  1. Sum-to-Product Formulas

📝 Note

  1. Difference-to-Product Formulas

📝 Note

  1. Double Angle Identities

Pythagorean Identities

  1. Cofunction Identity

These identities are used to convert between sine and cosine in situations where one is more convenient to use.

  1. Reciprocal Identity

These identities are used to simplify expressions and to find the inverse trigonometric functions.

  1. Quotient Identity

📝 Note

  1. Fundamental Integrals

Trigonometric Integral relationships

Even More Relationships!

  1. Constant Multiple Rule:

📝 Note!
K is a constant

  1. Sum Rule

  1. Difference Rule

  1. Power Rule

  1. Logarithmic Rule

  1. Exponential Rule

  1. Integral of constant raised to a variable

📝 Note!
a>0, a!=1

Other Hyperbolic Trigonometric Relationships

Even more integrals:

  1. Integration by Parts

📝 Note!

  1. For Trigonometric Substitution:

Then use trigonometric identities to integrate.

  1. Improper Integral:

  1. Beta Function:

📝 Note

  1. In physics, the beta function is used to compute and represent the scatter amplitude of a quantum hadro-dynamic concept known as Regge trajectory
  2. Used in calculus applications
  1. The beta function can also be used to evaluate the cumulative distribution function of a beta distribution.

  1. Gamma Function:

📝 Note

  1. Elliptic Integral:

📝 Note