code: def dup_integrate(f, m, K):
      """
      Computes the indefinite integral of ``f`` in ``K[x]``.
  
      Examples
      ========
  
      >>> from sympy.polys import ring, QQ
      >>> R, x = ring("x", QQ)
  
      >>> R.dup_integrate(x**2 + 2*x, 1)
      1/3*x**3 + x**2
      >>> R.dup_integrate(x**2 + 2*x, 2)
      1/12*x**4 + 1/3*x**3
  
      """
      if m <= 0 or not f:
          return f
  
      g = [K.zero] * m
  
      for i, c in enumerate(reversed(f)):
          n = i + 1
  
          for j in range(1, m):
              n *= i + j + 1
  
          g.insert(0, K.exquo(c, K(n)))
  
      return g
  
imports: from sympy.polys.densearith import dup_add_term, dmp_add_term, dup_lshift, dup_add, dmp_add, dup_sub, dmp_sub, dup_mul, dmp_mul, dup_sqr, dup_div, dup_rem, dmp_rem, dmp_expand, dup_mul_ground, dmp_mul_ground, dup_quo_ground, dmp_quo_ground, dup_exquo_ground, dmp_exquo_ground
  from sympy.polys.densebasic import dup_strip, dmp_strip, dup_convert, dmp_convert, dup_degree, dmp_degree, dmp_to_dict, dmp_from_dict, dup_LC, dmp_LC, dmp_ground_LC, dup_TC, dmp_TC, dmp_zero, dmp_ground, dmp_zero_p, dup_to_raw_dict, dup_from_raw_dict, dmp_zeros
  from sympy.polys.polyerrors import MultivariatePolynomialError, DomainError
  from sympy.utilities import variations
  from math import ceil, log
label_desc: Use image node_id 1 for calling a global function with example usage: dup_integrate(f, m, K) and returns: g, f