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

## Trigonometric Relationships

**Sum-to-Product Formulas**

**Difference-to-Product Formulas**

**Double Angle Identities**

## Pythagorean Identities

**Cofunction Identity**

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

**Reciprocal Identity**

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

**Quotient Identity**

**Fundamental Integrals**

## Trigonometric Integral relationships

## Even More Relationships!

**Constant Multiple Rule:**

**Sum Rule**

**Difference Rule**

**Power Rule**

**Logarithmic Rule**

**Exponential Rule**

**Integral of constant raised to a variable**

## Other Hyperbolic Trigonometric Relationships

## Even more integrals:

- Integration by Parts

- For Trigonometric Substitution:

Then use trigonometric identities to integrate.

- Improper Integral:

**Beta Function:**

- In physics, the beta function is used to compute and represent the scatter amplitude of a quantum hadro-dynamic concept known as Regge trajectory
- Used in calculus applications

- The beta function can also be used to evaluate the cumulative distribution function of a beta distribution.

**Gamma Function:**

**Elliptic Integral:**