Upperbound for the definite integral $f(t)=\int_{2}^{t}\frac{\sin^{2}(\pi \frac{\Gamma ^{2}(x)}{x})}{\sin^{2}(\frac{\pi }{x})}dx$

Question

What is a good upper bound for this function? $$f(t)=\int_{2}^{t}\frac{\sin^{2}(\pi \frac{\Gamma ^{2}(x)}{x})}{\sin^{2}(\frac{\pi }{x})}dx$$

I managed to find this.

$$f(t)=\int_{2}^{t}\frac{\beta ^{2}(\frac{\Gamma ^{2}(x)}{x},1-\frac{\Gamma ^{2}(x)}{x})}{\beta ^{2}(\frac{1}{x},1-\frac{1}{x})}dx$$

But i don't know what to do next.