Module integrate 

Symbolic integration (rule-based / heuristic).

Algorithm stack (increasing strength):

1. Linearity — sum, constant factor
2. Elementary templates — polynomials, 1/x, sin/cos/exp/tan/ln with affine inner k*x+b
3. Products — e^{ax+b}×sin/cos(cx+d), sin^m cos^n, x^n ln x, sin(ax+b)cos(cx+d)
4. Powers — (x+c)^n, sin^n/cos^n/tan^n/sec^n reductions, cos⁻² → tan
5. Rational — c/(x-a), 1/((x-a)(x-b)), P/Q partial fractions (deg Q ≤ 6), atan for 1/(x²+a²)
6. Substitution — u^n u', elementary f(u)·u'
7. Integration by parts — depth-limited, with direct integrate fallback

Not implemented: full Risch decision procedure, algebraic extensions, or RUBI-scale rule databases.

Enums

IntegrateError

Functions

contains_var

integrate