Convergence of the integral $\int_{1}^{\infty}\frac{x^q}{e^{x^p |\sin x|^r}}$

Question

I'm trying to solve the following exercise: Study the convergence of following integral: $$\int_{1}^{\infty}\frac{x^q}{e^{x^p |\sin x|^r}}$$ What I have tried: Divided area in intervals $[\pi k ; \pi(k + 1)]$. On each interval $x^p \sim k^p; x^q \sim k^q$. Then I divided each interval in a half and used a fact that $\sin(\pi k + t) \sim t$. Thus i need to somehow estimate $$\int_{0}^{\pi/2}\frac{1}{e^{k^p t^r}}dt$$ At this stage I got stuck. Could someone provide me a hint how to move forward or suggest another solution?