Integrating over a variable and an Unknown

Question

I'm new to integration in Python, so bear with me. The code short, so I will post the whole thing:

h = 6.626E-34
c = 3.0E8
k = 1.3806E-23
import scipy.integrate
from scipy.integrate import quad
from math import exp, pi

def f(x, T):
    return 4*pi*h*c**2/(x**5*exp(h*c/(x*k*T))-1)

res = quad(f, 0.0, 000000.3)
print(res)

What I would like to do here is integrate over x and have python return a numerical value in terms of T. Obviously T is undefined here because T is an unknown for my problem. The above code returns:

TypeError                                 Traceback (most recent call last)
<ipython-input-55-4227cf12c600> in <module>
      2     return 4*pi*h*c**2/(x**5*exp(h*c/(x*k*T))-1)
      3 
----> 4 res = quad(f, 0.0, 000000.3)
      5 print(res)

~/anaconda3/lib/python3.7/site-packages/scipy/integrate/quadpack.py in quad(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)
    340     if weight is None:
    341         retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,
--> 342                        points)
    343     else:
    344         if points is not None:

~/anaconda3/lib/python3.7/site-packages/scipy/integrate/quadpack.py in _quad(func, a, b, args, full_output, epsabs, epsrel, limit, points)
    451     if points is None:
    452         if infbounds == 0:
--> 453             return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
    454         else:
    455             return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit)

TypeError: f() missing 1 required positional argument: 'T'

I'd appreciate any help!

Answer 1

As far as I know scipy doesn't support symbolic integration. For something like that sympy might be a better choice. Looking at that integral though, I'm not sure its representable in closed form.