definite integrals – How to prove the converge of a sequence?

Let $t_{n} = int_{1}^{n} (ln(x)^p) ,dx$, where $p < 0$ is any real number.

How can I prove that this sequence converges?

My attempt: Clearly, $t_{n} geq 0$, so by linearly property of riemann integrals $t_{n}$ is increasing. Then, if $t_{n}$ is bounded, it is also convergent. Can you find a bound?