Unfazed by its roots?

Which of the following statements is/are true?

(A) : If $P(x)$ is a quadratic polynomial with real roots, then $\int \frac1{P(x)} \, dx$ has a closed form .

(B) : If $P(x)$ is a quadratic polynomial with non-real roots, then $\int \frac1{P(x)} \, dx$ has a closed form.