# 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?