Rules of Integration by Anti-Differentiation

In order to simplify the task of finding integrals, some general rules by anti-differentiation are developed to help finding integrals with having to use the definition directly.

Indefinite Integral Properties

Some useful rules of indefinite integrals

1. Indefinite integrals of Derivatives of Polynomials

   1. Anti Differentiation of Derivative of Constant Function

      

      Derivative of Constant Function

      

   2. Anti Differentiation of Derivative of Linear Function

      

      Derivative of Linear Function

      

   3. Anti Differentiation of Derivative of Power Function

      

      Derivative of Power Function

      imply

   4. Anti Differentiation of Derivative of Identity Function, c=1

      

      Derivative of  Function x

      

2. Indefinite integrals of Derivatives of Trigonometric Functions

   1. Anti Differentiation of Derivative of Sine Function

      

      Derivative of Sine Function

      

   2. Anti Differentiation of Derivative of Cosine Function

      

      Derivative of Cosine Function

      

   3. Anti Differentiation of Derivative of Tangent Function

      

      Derivative of Tangent Function

      

   4. Anti Differentiation of Derivative of Cotangent Function

      

      Derivative of Cotangent Function

      

   5. Anti Differentiation of Derivative of Secant Function

      

      Derivative of Secant Function

      

   6. Anti Differentiation of Derivative of Cosecant Function

      

      Derivative of Cosecant Function

      

3. Indefinite integrals of Derivatives of Exponential and Logarithmic Functions

   1. Anti Differentiation of Derivative of Natural Exponential Function

      

      Derivative of Natural Exponential Function

      

   2. Anti Differentiation of Derivative of Exponential Function

      

      Derivative of Exponential Function

      imply

   3. Anti Differentiation of Derivative of Natural Logarithmic Function

      

      Derivative of Natural Logarithmic Function

      

   4. Anti Differentiation of Derivative of Logarithmic Function

      

      Derivative of Logarithmic Function

      imply

4. Indefinite integrals of Derivatives of Inverse Trigonometric Functions

   1. Anti Differentiation of Derivative of Inverse Sine Function

      

      Derivative of Inverse Sine Function

      

   2. Anti Differentiation of Derivative of Inverse Cosine Function

      

      Derivative of Inverse Cosine Function

      

   3. Anti Differentiation of Derivative of Inverse Tangent Function

      

      Derivative of Inverse Tangent Function

      

   4. Anti Differentiation of Derivative of Inverse Cotangent Function

      

      Derivative of Inverse Cotangent Function

      

   5. Anti Differentiation of Derivative of Inverse Secant Function

      

      Derivative of Inverse Secant Function

      

   6. Anti Differentiation of Derivative of Inverse Cosecant Function

      

      Derivative of Inverse Cosecant Function

      

Indefinite Integrals

Basic Forms