Fixed issue 26775

Author: hanspi42

sympy/integrals/laplace.py

@@ -2100,8 +2100,10 @@ def _inverse_laplace_rational(fn, s, t, plane, *, simplify):
         dc = [x/dc_lead for x in dc]
         nc = [x/dc_lead for x in n.as_poly(s).all_coeffs()]
         if len(dc) == 1:
-            r = nc[0]*DiracDelta(t)
-            terms_t.append(r)
+            N = len(nc)-1
+            for c in enumerate(nc):
+                r = c[1]*DiracDelta(t, N-c[0])
+                terms_t.append(r)
         elif len(dc) == 2:
             r = nc[0]*exp(-dc[1]*t)
             terms_t.append(Heaviside(t)*r)

sympy/integrals/tests/test_laplace.py

@@ -717,6 +717,9 @@ def simp_hyp(expr):
             Derivative(InverseLaplaceTransform(f(s), s, t, None), (t, 42)))
     assert ILT(cos(s), s, t) == InverseLaplaceTransform(cos(s), s, t, None)
     # Rules for testing different DiracDelta cases
+    assert (
+        ILT(1 + 2*s + 3*s**2 + 5*s**3, s, t) == DiracDelta(t) +
+        2*DiracDelta(t, 1) + 3*DiracDelta(t, 2) + 5*DiracDelta(t, 3))
     assert (ILT(2*exp(3*s) - 5*exp(-7*s), s, t) ==
             2*InverseLaplaceTransform(exp(3*s), s, t, None) -
             5*DiracDelta(t - 7))