closes sympy#15498

sympy/integrals/tests/test_heurisch.py

@@ -2,7 +2,7 @@
 from sympy.core.add import Add
 from sympy.core.function import (Derivative, Function, diff)
 from sympy.core.numbers import (I, Rational, pi)
-from sympy.core.relational import Ne
+from sympy.core.relational import Eq, Ne
 from sympy.core.symbol import (Symbol, symbols)
 from sympy.functions.elementary.exponential import (LambertW, exp, log)
 from sympy.functions.elementary.hyperbolic import (asinh, cosh, sinh, tanh)
@@ -12,6 +12,8 @@
 from sympy.functions.special.bessel import (besselj, besselk, bessely, jn)
 from sympy.functions.special.error_functions import erf
 from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import And
+from sympy.matrices import Matrix
 from sympy.simplify.ratsimp import ratsimp
 from sympy.simplify.simplify import simplify
 from sympy.integrals.heurisch import components, heurisch, heurisch_wrapper
@@ -378,3 +380,20 @@ def test_heurisch_complex_erf_issue_26338():
     assert heurisch(a, x, hints=[]) is None  # None, not a wrong soln
     a = sqrt(pi)*erf((1 + I)/2)/2
     assert integrate(exp(-I*x**2/2), (x, 0, 1)) == a - I*a
+
+
+def test_issue_15498():
+    Z0 = Function('Z0')
+    k01, k10, t, s= symbols('k01 k10 t s', real=True, positive=True)
+    m = Matrix([[exp(-k10*t)]])
+    _83 = Rational(83, 100)  # 0.83 works, too
+    [a, b, c, d, e, f, g] = [100, 0.5, _83, 50, 0.6, 2, 120]
+    AIF_btf = a*(d*e*(1 - exp(-(t - b)/e)) + f*g*(1 - exp(-(t - b)/g)))
+    AIF_atf = a*(d*e*exp(-(t - b)/e)*(exp((c - b)/e) - 1
+        ) + f*g*exp(-(t - b)/g)*(exp((c - b)/g) - 1))
+    AIF_sym = Piecewise((0, t < b), (AIF_btf, And(b <= t, t < c)), (AIF_atf, c <= t))
+    aif_eq = Eq(Z0(t), AIF_sym)
+    f_vec = Matrix([[k01*Z0(t)]])
+    integrand = m*m.subs(t, s)**-1*f_vec.subs(aif_eq.lhs, aif_eq.rhs).subs(t, s)
+    solution = integrate(integrand[0], (s, 0, t))
+    assert solution is not None  # does not hang and takes less than 10 s