Answer

The denominator of the integrand factors as

x² – 2x – 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