Integral form
Indefinite integrals
Rational and Irrational FUNCTIONS
Contain ax + b
Contain √ (ax + b)
Containing 2 ± x ^ a ^ 2
They contain a ^ 2-x ^ 2, x Contain √ (x ^ 2 ± a ^ 2)
Contienen√ (a ^ 2 ± x ^ 2)
They contain ax ^ 2 + bx + c
Contain √ (ax ^ 2 + bx + c)

TRIGONOMETRIC FUNCTIONS
contain sin⁡ax
contain cos⁡ax
Tan⁡ax contain or cot⁡ax
Sec⁡ax contain or csc⁡ax
several functions
Inverse trigonometric functions

Power Functions and / or logarithmic

hyperbolic Functions
Inverse Hyperbolic Functions

Definite integrals

Integration Methods
Integration by parts
SUBSTITUTE FOR INTEGRATION
Integration of rational functions
METHOD HERMITE
INTEGRATION Irrational algebraic functions
INTEGRATION transcendental functions
Integration of trigonometric functions

ORDINARY DIFFERENTIAL EQUATIONS
Linear Differential Equations

NUMERICAL SOLUTION DIFFERENTIAL EQUATIONS
Runge-Kutta methods FOURTH ORDER