Say I have the following expression which I would like to integrate over the variable z from 0 to L.
import sympy as sp
mdot, D, R, alpha, beta, xi, mu0, q, cp, Tin, L = sp.symbols("\dot{m}, D, R, alpha, beta, xi, mu_0, q, c_p, T_in, L", real=True, positive=True, constant=True)
z = sp.symbols("z", real=True, positive=True)
n = sp.Symbol("n", real=True)
firstexpr = 8 * mdot**2 * R / (sp.pi**2 * D**5) * (alpha + beta * (sp.pi * D * mu0 / (4 * mdot))**xi * (q * z / (mdot * cp) + Tin)**(n * xi)) * (q * z / (mdot * cp) + Tin)
res1 = sp.integrate(firstexpr, (z, 0, L), conds="none")
This will take forever: I had to stop the computation after 10 minutes on my pc without getting an answer.
Situation improves dramatically if I rewrite my expression so that it contains only the minimum number of constant symbols, integrating it, and finally substituting the original symbols:
a = 8 * mdot**2 * R / (sp.pi**2 * D**5)
b = beta * (sp.pi * D * mu0 / (4 * mdot))**xi
c = q / (mdot * cp)
_a, _b, _c = sp.symbols("a, b, c", real=True, positive=True, constant=True)
secondexpr = _a * (alpha + _b * (_c * z + Tin)**(n * xi)) * (_c * z + Tin)
res2 = sp.integrate(secondexpr, (z, 0, L), conds="none")
sp.simplify(res2.subs([(_a, a), (_b, b), (_c, c)]))
Why is sympy taking extremely long time in the first case? Did I miss some assumption in the creation of my symbols?
