Split the integral
into a sum of integrals that are each improper for only one reason.

Answer

The denominator of the integrand factors as

*x*^{2} – 2*x* – 15 = (*x* – 5)(*x* + 3).

Looking at this, and at the graph, we can see that the integrand is badly behaved at *x* = -3 and at *x* = 5. We need to split the integral at *x* = -3 and at some point between *x* = -3 and *x* = 5 (again, we may as well take *x* = 0). Then