mosaic (version 0.9-0)

symbolicInt: Find the symbolic integral of a formula

Description

Find the symbolic integral of a formula

Use recursion to find a symbolic antiderivative

Attempts symbolic integration of some mathematical/arithmetical forms

Attempts symbolic integration of some mathematical forms

Attempts symbolic integration of some mathematical forms using trigonometric substitution

Takes a call and returns its affine coefficients.

Usage

symbolicInt(form, ...)
symbolicAntiD(form, ...)
.intArith(form, ...)
.intMath(form, ...)
.intTrig(form, num, den, .x.)
.affine.exp(tree, .x.)

Arguments

form

an object of type formula to be integrated. Rhs of formula indicates which variable to integrate with respect to. Must only have one variable.

...

extra parameters

num

numerator

den

denominator

.x.

the variable name

tree

the expression to be analyzed

Value

• symbolicInt returns a function whose body is the symbolic antiderivative of the formula. If this method does not recognize the formula, it will return an error.

  a formula implementing giving symbolic anti-derivative. If the formula isn't found by the algorithm, an error is thrown.

  An expression with the integral, or throws an error if unsuccessful.

  An expression with the integral, or throws an error if unsuccessful.

  An expression with the integral, or throws an error if unsuccessful.

  A list with values of a and b satisfying a*.x.+b = tree. If the expression is not affine, returns an empty list.

Details

This symbolic integrator recognizes simple polynomials and functions such as sin, cos, tan, sinh, cosh, tanh, sqrt, and exp.

It will not perform more complicated substitutions or integration by parts.