API

integrate(eq, x; kwargs...)

is the main entry point to integrate a univariate expression eq with respect to `x' (optional).

julia> using Symbolics, SymbolNumericIntegration

julia> @variables x a

julia> integrate(x * sin(2x))
((1//4)*sin(2x) - (1//2)*x*cos(2x), 0, 0)

julia> integrate(x * sin(a * x), x; symbolic = true, detailed = false)
(sin(a*x) - a*x*cos(a*x)) / (a^2)

julia> integrate(x * sin(a * x), (x, 0, 1); symbolic = true, detailed = false)
(sin(a) - a*cos(a)) / (a^2)

Arguments:

• eq: a univariate expression
• x: independent variable (optional if eq is univariate) or a tuple of (independent variable, lower bound, upper bound) for definite integration.

Keyword Arguments:

• abstol (default: 1e-6): the desired tolerance
• num_steps (default: 2): the number of different steps with expanding basis to be tried
• num_trials (default: 10): the number of trials in each step (no changes to the basis)
• show_basis (default: false): if true, the basis (list of candidate terms) is printed
• bypass (default: false): if true do not integrate terms separately but consider all at once
• symbolic (default: false): try symbolic integration first (will be forced if eq has symbolic constants)
• max_basis (default: 100): the maximum number of candidate terms to consider
• verbose (default: false): print a detailed report
• complex_plane (default: true): generate random test points on the complex plane (if false, the points will be on real axis)
• radius (default: 1.0): the radius of the disk in the complex plane to generate random test points
• opt (default: STLSQ(exp.(-10:1:0))): the sparse regression optimizer (from DataDrivenSparse)
• homotopy (default: true): deprecated, will be removed in a future version
• use_optim (default: false): deprecated, will be removed in a future version
• detailed (default: true): (solved, unsolved, err) output format. If detailed=false, only the final integral is returned.

Returns a tuple of (solved, unsolved, err) if detailed == true, where

solved: the solved integral 
unsolved: the residual unsolved portion of the input
err: the numerical error in reaching the solution

Returns the resulting integral or nothing if detailed == false