import sympy as sp

x, t = sp.symbols('x t')

integrand = t / (1 + t**2 * sp.sin(t)**2)

integral_expr = sp.integrate(integrand, (t, 0, x))

limit_expr = sp.limit(integral_expr / x, x, sp.oo)

limit_expr

{
	"name": "NotImplementedError",
	"message": "Don't know how to calculate the mrv of 'Integral(t/(t**2*sin(t)**2 + 1), (t, 0, _p))'",
	"stack": "---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Cell In[3], line 9
      5 integrand = t / (1 + t**2 * sp.sin(t)**2)
      7 integral_expr = sp.integrate(integrand, (t, 0, x))
----> 9 limit_expr = sp.limit(integral_expr / x, x, sp.oo)
     11 limit_expr

File ~/myenv/lib64/python3.12/site-packages/sympy/series/limits.py:64, in limit(e, z, z0, dir)
     13 def limit(e, z, z0, dir=\"+\"):
     14     \"\"\"Computes the limit of ``e(z)`` at the point ``z0``.
     15 
     16     Parameters
   (...)
     61      limit_seq : returns the limit of a sequence.
     62     \"\"\"
---> 64     return Limit(e, z, z0, dir).doit(deep=False)

File ~/myenv/lib64/python3.12/site-packages/sympy/series/limits.py:375, in Limit.doit(self, **hints)
    372 l = None
    374 try:
--> 375     r = gruntz(e, z, z0, dir)
    376     if r is S.NaN or l is S.NaN:
    377         raise PoleError()

File ~/myenv/lib64/python3.12/site-packages/sympy/series/gruntz.py:733, in gruntz(e, z, z0, dir)
    730     else:
    731         raise NotImplementedError(\"dir must be '+' or '-'\")
--> 733 r = limitinf(e0, z)
    735 # This is a bit of a heuristic for nice results... we always rewrite
    736 # tractable functions in terms of familiar intractable ones.
    737 # It might be nicer to rewrite the exactly to what they were initially,
    738 # but that would take some work to implement.
    739 return r.rewrite('intractable', deep=True)

File ~/myenv/lib64/python3.12/site-packages/sympy/core/cache.py:72, in __cacheit.<locals>.func_wrapper.<locals>.wrapper(*args, **kwargs)
     69 @wraps(func)
     70 def wrapper(*args, **kwargs):
     71     try:
---> 72         retval = cfunc(*args, **kwargs)
     73     except TypeError as e:
     74         if not e.args or not e.args[0].startswith('unhashable type:'):

File ~/myenv/lib64/python3.12/site-packages/sympy/series/gruntz.py:453, in limitinf(e, x)
    451     c0, e0 = mrv_leadterm(e.min, x)
    452 else:
--> 453     c0, e0 = mrv_leadterm(e, x)
    454 sig = sign(e0, x)
    455 if sig == 1:

File ~/myenv/lib64/python3.12/site-packages/sympy/core/cache.py:72, in __cacheit.<locals>.func_wrapper.<locals>.wrapper(*args, **kwargs)
     69 @wraps(func)
     70 def wrapper(*args, **kwargs):
     71     try:
---> 72         retval = cfunc(*args, **kwargs)
     73     except TypeError as e:
     74         if not e.args or not e.args[0].startswith('unhashable type:'):

File ~/myenv/lib64/python3.12/site-packages/sympy/series/gruntz.py:536, in mrv_leadterm(e, x)
    534     return (e, S.Zero)
    535 if Omega == SubsSet():
--> 536     Omega, exps = mrv(e, x)
    537 if not Omega:
    538     # e really does not depend on x after simplification
    539     return exps, S.Zero

File ~/myenv/lib64/python3.12/site-packages/sympy/series/gruntz.py:267, in mrv(e, x)
    265     a, b = d.as_two_terms()
    266     s1, e1 = mrv(a, x)
--> 267     s2, e2 = mrv(b, x)
    268     return mrv_max1(s1, s2, e.func(i, e1, e2), x)
    269 elif e.is_Pow and e.base != S.Exp1:

File ~/myenv/lib64/python3.12/site-packages/sympy/series/gruntz.py:320, in mrv(e, x)
    317 elif e.is_Derivative:
    318     raise NotImplementedError(\"MRV set computation for derivatives\"
    319                               \" not implemented yet.\")
--> 320 raise NotImplementedError(
    321     \"Don't know how to calculate the mrv of '%s'\" % e)

NotImplementedError: Don't know how to calculate the mrv of 'Integral(t/(t**2*sin(t)**2 + 1), (t, 0, _p))'"
}