code: def integrate(
      *args,
      meijerg=None,
      conds="piecewise",
      risch=None,
      heurisch=None,
      manual=None,
      **kwargs,
  ):
      """integrate(f, var, ...)
  
      .. deprecated:: 1.6
  
         Using ``integrate()`` with :class:`~.Poly` is deprecated. Use
         :meth:`.Poly.integrate` instead. See :ref:`deprecated-integrate-poly`.
  
      Explanation
      ===========
  
      Compute definite or indefinite integral of one or more variables
      using Risch-Norman algorithm and table lookup. This procedure is
      able to handle elementary algebraic and transcendental functions
      and also a huge class of special functions, including Airy,
      Bessel, Whittaker and Lambert.
  
      var can be:
  
      - a symbol                   -- indefinite integration
      - a tuple (symbol, a)        -- indefinite integration with result
                                      given with ``a`` replacing ``symbol``
      - a tuple (symbol, a, b)     -- definite integration
  
      Several variables can be specified, in which case the result is
      multiple integration. (If var is omitted and the integrand is
      univariate, the indefinite integral in that variable will be performed.)
  
      Indefinite integrals are returned without terms that are independent
      of the integration variables. (see examples)
  
      Definite improper integrals often entail delicate convergence
      conditions. Pass conds='piecewise', 'separate' or 'none' to have
      these returned, respectively, as a Piecewise function, as a separate
      result (i.e. result will be a tuple), or not at all (default is
      'piecewise').
  
      **Strategy**
  
      SymPy uses various approaches to definite integration. One method is to
      find an antiderivative for the integrand, and then use the fundamental
      theorem of calculus. Various functions are implemented to integrate
      polynomial, rational and trigonometric functions, and integrands
      containing DiracDelta terms.
  
      SymPy also implements the part of the Risch algorithm, which is a decision
      procedure for integrating elementary functions, i.e., the algorithm can
      either find an elementary antiderivative, or prove that one does not
      exist.  There is also a (very successful, albeit somewhat slow) general
      implementation of the heuristic Risch algorithm.  This algorithm will
      eventually be phased out as more of the full Risch algorithm is
      implemented. See the docstring of Integral._eval_integral() for more
      details on computing the antiderivative using algebraic methods.
  
      The option risch=True can be used to use only the (full) Risch algorithm.
      This is useful if you want to know if an elementary function has an
      elementary antiderivative.  If the indefinite Integral returned by this
      function is an instance of NonElementaryIntegral, that means that the
      Risch algorithm has proven that integral to be non-elementary.  Note that
      by default, additional methods (such as the Meijer G method outlined
      below) are tried on these integrals, as they may be expressible in terms
      of special functions, so if you only care about elementary answers, use
      risch=True.  Also note that an unevaluated Integral returned by this
      function is not necessarily a NonElementaryIntegral, even with risch=True,
      as it may just be an indication that the particular part of the Risch
      algorithm needed to integrate that function is not yet implemented.
  
      Another family of strategies comes from re-writing the integrand in
      terms of so-called Meijer G-functions. Indefinite integrals of a
      single G-function can always be computed, and the definite integral
      of a product of two G-functions can be computed from zero to
      infinity. Various strategies are implemented to rewrite integrands
      as G-functions, and use this information to compute integrals (see
      the ``meijerint`` module).
  
      The option manual=True can be used to use only an algorithm that tries
      to mimic integration by hand. This algorithm does not handle as many
      integrands as the other algorithms implemented but may return results in
      a more familiar form. The ``manualintegrate`` module has functions that
      return the steps used (see the module docstring for more information).
  
      In general, the algebraic methods work best for computing
      antiderivatives of (possibly complicated) combinations of elementary
      functions. The G-function methods work best for computing definite
      integrals from zero to infinity of moderately complicated
      combinations of special functions, or indefinite integrals of very
      simple combinations of special functions.
  
      The strategy employed by the integration code is as follows:
  
      - If computing a definite integral, and both limits are real,
        and at least one limit is +- oo, try the G-function method of
        definite integration first.
  
      - Try to find an antiderivative, using all available methods, ordered
        by performance (that is try fastest method first, slowest last; in
        particular polynomial integration is tried first, Meijer
        G-functions second to last, and heuristic Risch last).
  
      - If still not successful, try G-functions irrespective of the
        limits.
  
      The option meijerg=True, False, None can be used to, respectively:
      always use G-function methods and no others, never use G-function
      methods, or use all available methods (in order as described above).
      It defaults to None.
  
      Examples
      ========
  
      >>> from sympy import integrate, log, exp, oo
      >>> from sympy.abc import a, x, y
  
      >>> integrate(x*y, x)
      x**2*y/2
  
      >>> integrate(log(x), x)
      x*log(x) - x
  
      >>> integrate(log(x), (x, 1, a))
      a*log(a) - a + 1
  
      >>> integrate(x)
      x**2/2
  
      Terms that are independent of x are dropped by indefinite integration:
  
      >>> from sympy import sqrt
      >>> integrate(sqrt(1 + x), (x, 0, x))
      2*(x + 1)**(3/2)/3 - 2/3
      >>> integrate(sqrt(1 + x), x)
      2*(x + 1)**(3/2)/3
  
      >>> integrate(x*y)
      Traceback (most recent call last):
      ...
      ValueError: specify integration variables to integrate x*y
  
      Note that ``integrate(x)`` syntax is meant only for convenience
      in interactive sessions and should be avoided in library code.
  
      >>> integrate(x**a*exp(-x), (x, 0, oo)) # same as conds='piecewise'
      Piecewise((gamma(a + 1), re(a) > -1),
          (Integral(x**a*exp(-x), (x, 0, oo)), True))
  
      >>> integrate(x**a*exp(-x), (x, 0, oo), conds='none')
      gamma(a + 1)
  
      >>> integrate(x**a*exp(-x), (x, 0, oo), conds='separate')
      (gamma(a + 1), re(a) > -1)
  
      See Also
      ========
  
      Integral, Integral.doit
  
      """
      doit_flags = {
          "deep": False,
          "meijerg": meijerg,
          "conds": conds,
          "risch": risch,
          "heurisch": heurisch,
          "manual": manual,
      }
      integral = Integral(*args, **kwargs)
  
      if isinstance(integral, Integral):
          return integral.doit(**doit_flags)
      else:
          new_args = [
              a.doit(**doit_flags) if isinstance(a, Integral) else a
              for a in integral.args
          ]
          return integral.func(*new_args)
  
imports: from typing import Tuple
  from sympy.concrete.expr_with_limits import AddWithLimits
  from sympy.core.add import Add
  from sympy.core.basic import Basic
  from sympy.core.containers import Tuple
  from sympy.core.expr import Expr
  from sympy.core.exprtools import factor_terms
  from sympy.core.function import diff
  from sympy.core.logic import fuzzy_bool
  from sympy.core.mul import Mul
  from sympy.core.numbers import oo, pi
  from sympy.core.relational import Ne
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol, Wild
  from sympy.core.sympify import sympify
  from sympy.functions import Piecewise, sqrt, piecewise_fold, tan, cot, atan
  from sympy.functions.elementary.exponential import log
  from sympy.functions.elementary.integers import floor
  from sympy.functions.elementary.complexes import Abs, sign
  from sympy.functions.elementary.miscellaneous import Min, Max
  from sympy.functions.special.singularity_functions import Heaviside
  from .rationaltools import ratint
  from sympy.matrices import MatrixBase
  from sympy.polys import Poly, PolynomialError
  from sympy.series.formal import FormalPowerSeries
  from sympy.series.limits import limit
  from sympy.series.order import Order
  from sympy.tensor.functions import shape
  from sympy.utilities.exceptions import sympy_deprecation_warning
  from sympy.utilities.iterables import is_sequence
  from sympy.utilities.misc import filldedent
  from .deltafunctions import deltaintegrate
  from .meijerint import meijerint_definite, meijerint_indefinite, _debug
  from .trigonometry import trigintegrate
label_desc: Use image node_id 1 for calling a global function with example usage: integrate() and returns: integral, integral