Rubi’s Integration Rules

Rubi systematically applies precisely defined rules to efficiently integrate large classes of mathematical expressions. All the integration rules are displayed in human readable form as PDF files and organized in a hierarchical tree based on the form of the integrand.

The rules are displayed in mathematical notation followed by the equivalent Mathematica program code. Comments preceding many of the rules document them as follows:

1 Algebraic Function Rules

1.1 Binomial products

1.1.1 Linear

1.1.2 Quadratic

1.1.3 General

1.1.4 Improper

1.2 Trinomial products

1.2.1 Quadratic

1.2.2 Quartic

1.2.3 General

1.2.4 Improper

1.3 Miscellaneous

2 Exponential Rules

3 Logarithm Rules

4 Trig Function Rules

4.1 Sine

4.3 Tangent

4.5 Secant

4.7 Miscellaneous

5 Inverse Trig Function Rules

5.1 Inverse sine

5.3 Inverse tangent

5.5 Inverse secant

6 Hyperbolic Function Rules

6.1 Hyperbolic sine

6.3 Hyperbolic tangent

6.5 Hyperbolic secant

6.7 Miscellaneous

7 Inverse Hyperbolic Function Rules

7.1 Inverse hyperbolic sine

7.3 Inverse hyperbolic tangent

7.5 Inverse hyperbolic secant

8 Special Function Rules

9 Miscellaneous Rules