جبر رایانه‌ای

>>> from sympy import init_printing, integrate, Symbol, exp, cos, erf >>> init_printing() >>> x = Symbol("x") >>> # Polynomial Function >>> f = x**2 + x + 1 >>> f  2         x  + x + 1 >>> integrate(f, x)  3    2     x    x      ── + ── + x 3    2      >>> # Rational Function >>> f = x / (x**2 + 2 * x + 1) >>> f      x       ────────────  2           x  + 2⋅x + 1  >>> integrate(f, x)                1   log(x + 1) + ─────              x + 1 >>> # Exponential-polynomial functions >>> f = x**2 * exp(x) * cos(x) >>> f  2  x        x ⋅ℯ ⋅cos(x) >>> integrate(f, x)  2  x           2  x                         x           x        x ⋅ℯ ⋅sin(x)   x ⋅ℯ ⋅cos(x)      x          ℯ ⋅sin(x)   ℯ ⋅cos(x) ──────────── + ──────────── - x⋅ℯ ⋅sin(x) + ───────── - ─────────      2              2                           2           2     >>> # A non-elementary integral >>> f = exp(-(x**2)) * erf(x) >>> f    2         -x         ℯ   ⋅erf(x) >>> integrate(f, x)    ___    2    ╲╱ π ⋅erf (x) ─────────────       4