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Rules of Integration by Anti-Differentiation
  Indefinite Integral Properties

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

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      Derivative of Constant Function

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    2. Anti Differentiation of Derivative of Linear Function

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      Derivative of Linear Function

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    3. Anti Differentiation of Derivative of Power Function

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      Derivative of Power Function

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

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      Derivative of  Function x

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  2. Indefinite integrals of Derivatives of Trigonometric Functions

    1. Anti Differentiation of Derivative of Sine Function

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      Derivative of Sine Function

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    2. Anti Differentiation of Derivative of Cosine Function

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      Derivative of Cosine Function

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    3. Anti Differentiation of Derivative of Tangent Function

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      Derivative of Tangent Function

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    4. Anti Differentiation of Derivative of Cotangent Function

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      Derivative of Cotangent Function

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    5. Anti Differentiation of Derivative of Secant Function

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      Derivative of Secant Function

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    6. Anti Differentiation of Derivative of Cosecant Function

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      Derivative of Cosecant Function

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  3. Indefinite integrals of Derivatives of Exponential and Logarithmic Functions

    1. Anti Differentiation of Derivative of Natural Exponential Function

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      Derivative of Natural Exponential Function

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    2. Anti Differentiation of Derivative of Exponential Function

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      Derivative of Exponential Function

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    3. Anti Differentiation of Derivative of Natural Logarithmic Function

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      Derivative of Natural Logarithmic Function

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    4. Anti Differentiation of Derivative of Logarithmic Function

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      Derivative of Logarithmic Function

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  4. Indefinite integrals of Derivatives of Inverse Trigonometric Functions

    1. Anti Differentiation of Derivative of Inverse Sine Function

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      Derivative of Inverse Sine Function

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    2. Anti Differentiation of Derivative of Inverse Cosine Function

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      Derivative of Inverse Cosine Function

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    3. Anti Differentiation of Derivative of Inverse Tangent Function

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      Derivative of Inverse Tangent Function

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    4. Anti Differentiation of Derivative of Inverse Cotangent Function

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      Derivative of Inverse Cotangent Function

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    5. Anti Differentiation of Derivative of Inverse Secant Function

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      Derivative of Inverse Secant Function

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    6. Anti Differentiation of Derivative of Inverse Cosecant Function

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      Derivative of Inverse Cosecant Function

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ID: 111000021 Last Updated: 10/22/2011 Revision: 0 Ref:

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References

  1. S. James, 1999, Calculus
  2. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering
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